Results of Orthogonal Polynomials II

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
18.17.E1	${\displaystyle{\displaystyle 2n\int_{0}^{x}(1-y)^{\alpha}(1+y)^{\beta}P^{(\alpha,\beta)}_{n}\left(y\right)\mathrm{d}y=P^{(\alpha+1,\beta+1)}_{n-1}\left(0\right)-(1-x)^{\alpha+1}(1+x)^{\beta+1}P^{(\alpha+1,\beta+1)}_{n-1}\left(x\right)}}$ 2n\int_{0}^{x}(1-y)^{\alpha}(1+y)^{\beta}\JacobipolyP{\alpha}{\beta}{n}@{y}\diff{y} = \JacobipolyP{\alpha+1}{\beta+1}{n-1}@{0}-(1-x)^{\alpha+1}(1+x)^{\beta+1}\JacobipolyP{\alpha+1}{\beta+1}{n-1}@{x}		2*n*int((1 - y)^(alpha)*(1 + y)^(beta)* JacobiP(n, alpha, beta, y), y = 0..x) = JacobiP(n - 1, alpha + 1, beta + 1, 0)-(1 - x)^(alpha + 1)*(1 + x)^(beta + 1)* JacobiP(n - 1, alpha + 1, beta + 1, x)	2*n*Integrate[(1 - y)^\[Alpha]*(1 + y)^\[Beta]* JacobiP[n, \[Alpha], \[Beta], y], {y, 0, x}, GenerateConditions->None] == JacobiP[n - 1, \[Alpha]+ 1, \[Beta]+ 1, 0]-(1 - x)^(\[Alpha]+ 1)*(1 + x)^(\[Beta]+ 1)* JacobiP[n - 1, \[Alpha]+ 1, \[Beta]+ 1, x]	Failure	Successful	Manual Skip!	Successful [Tested: 81]
18.17.E2	${\displaystyle{\displaystyle\int_{0}^{x}L_{m}\left(y\right)L_{n}\left(x-y\right)\mathrm{d}y=\int_{0}^{x}L_{m+n}\left(y\right)\mathrm{d}y}}$ \int_{0}^{x}\LaguerrepolyL[]{m}@{y}\LaguerrepolyL[]{n}@{x-y}\diff{y} = \int_{0}^{x}\LaguerrepolyL[]{m+n}@{y}\diff{y}		int(LaguerreL(m, y)*LaguerreL(n, x - y), y = 0..x) = int(LaguerreL(m + n, y), y = 0..x)	Integrate[LaguerreL[m, y]*LaguerreL[n, x - y], {y, 0, x}, GenerateConditions->None] == Integrate[LaguerreL[m + n, y], {y, 0, x}, GenerateConditions->None]	Failure	Failure	Successful [Tested: 27]	Successful [Tested: 27]
18.17.E2	${\displaystyle{\displaystyle\int_{0}^{x}L_{m+n}\left(y\right)\mathrm{d}y=L_{m+n}\left(x\right)-L_{m+n+1}\left(x\right)}}$ \int_{0}^{x}\LaguerrepolyL[]{m+n}@{y}\diff{y} = \LaguerrepolyL[]{m+n}@{x}-\LaguerrepolyL[]{m+n+1}@{x}		int(LaguerreL(m + n, y), y = 0..x) = LaguerreL(m + n, x)- LaguerreL(m + n + 1, x)	Integrate[LaguerreL[m + n, y], {y, 0, x}, GenerateConditions->None] == LaguerreL[m + n, x]- LaguerreL[m + n + 1, x]	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 27]
18.17.E3	${\displaystyle{\displaystyle\int_{0}^{x}H_{n}\left(y\right)\mathrm{d}y=\frac{1}{2(n+1)}(H_{n+1}\left(x\right)-H_{n+1}\left(0\right))}}$ \int_{0}^{x}\HermitepolyH{n}@{y}\diff{y} = \frac{1}{2(n+1)}(\HermitepolyH{n+1}@{x}-\HermitepolyH{n+1}@{0})		int(HermiteH(n, y), y = 0..x) = (1)/(2*(n + 1))*(HermiteH(n + 1, x)- HermiteH(n + 1, 0))	Integrate[HermiteH[n, y], {y, 0, x}, GenerateConditions->None] == Divide[1,2*(n + 1)]*(HermiteH[n + 1, x]- HermiteH[n + 1, 0])	Failure	Successful	Failed [9 / 9] Result: Float(undefined)+Float(undefined)*I Test Values: {x = 3/2, n = 1} Result: -1.500000000+0.*I Test Values: {x = 3/2, n = 2} ... skip entries to safe data	Successful [Tested: 9]
18.17.E4	${\displaystyle{\displaystyle\int_{0}^{x}e^{-y^{2}}H_{n}\left(y\right)\mathrm{d}y=H_{n-1}\left(0\right)-e^{-x^{2}}H_{n-1}\left(x\right)}}$ \int_{0}^{x}e^{-y^{2}}\HermitepolyH{n}@{y}\diff{y} = \HermitepolyH{n-1}@{0}-e^{-x^{2}}\HermitepolyH{n-1}@{x}		int(exp(- (y)^(2))*HermiteH(n, y), y = 0..x) = HermiteH(n - 1, 0)- exp(- (x)^(2))*HermiteH(n - 1, x)	Integrate[Exp[- (y)^(2)]*HermiteH[n, y], {y, 0, x}, GenerateConditions->None] == HermiteH[n - 1, 0]- Exp[- (x)^(2)]*HermiteH[n - 1, x]	Failure	Successful	Successful [Tested: 9]	Failed [3 / 9] Result: Indeterminate Test Values: {Rule[n, 2], Rule[x, 1.5]} Result: Indeterminate Test Values: {Rule[n, 2], Rule[x, 0.5]} ... skip entries to safe data
18.17.E5	${\displaystyle{\displaystyle\frac{C^{(\lambda)}_{n}\left(\cos\theta_{1}\right)}{C^{(\lambda)}_{n}\left(1\right)}\frac{C^{(\lambda)}_{n}\left(\cos\theta_{2}\right)}{C^{(\lambda)}_{n}\left(1\right)}=\frac{\Gamma\left(\lambda+\frac{1}{2}\right)}{\pi^{\frac{1}{2}}\Gamma\left(\lambda\right)}\*\int_{0}^{\pi}\frac{C^{(\lambda)}_{n}\left(\cos\theta_{1}\cos\theta_{2}+\sin\theta_{1}\sin\theta_{2}\cos\phi\right)}{C^{(\lambda)}_{n}\left(1\right)}(\sin\phi)^{2\lambda-1}\mathrm{d}\phi}}$ \frac{\ultrasphpoly{\lambda}{n}@{\cos@@{\theta_{1}}}}{\ultrasphpoly{\lambda}{n}@{1}}\frac{\ultrasphpoly{\lambda}{n}@{\cos@@{\theta_{2}}}}{\ultrasphpoly{\lambda}{n}@{1}} = \frac{\EulerGamma@{\lambda+\frac{1}{2}}}{\pi^{\frac{1}{2}}\EulerGamma@{\lambda}}\*\int_{0}^{\pi}\frac{\ultrasphpoly{\lambda}{n}@{\cos@@{\theta_{1}}\cos@@{\theta_{2}}+\sin@@{\theta_{1}}\sin@@{\theta_{2}}\cos@@{\phi}}}{\ultrasphpoly{\lambda}{n}@{1}}(\sin@@{\phi})^{2\lambda-1}\diff{\phi}	${\displaystyle{\displaystyle\lambda>0,\Re(\lambda+\frac{1}{2})>0,\Re(\lambda)>0}}$	(GegenbauerC(n, lambda, cos(theta[1])))/(GegenbauerC(n, lambda, 1))*(GegenbauerC(n, lambda, cos(theta[2])))/(GegenbauerC(n, lambda, 1)) = (GAMMA(lambda +(1)/(2)))/((Pi)^((1)/(2))* GAMMA(lambda))* int((GegenbauerC(n, lambda, cos(theta[1])*cos(theta[2])+ sin(theta[1])*sin(theta[2])*cos(phi)))/(GegenbauerC(n, lambda, 1))*(sin(phi))^(2*lambda - 1), phi = 0..Pi)	Divide[GegenbauerC[n, \[Lambda], Cos[Subscript[\[Theta], 1]]],GegenbauerC[n, \[Lambda], 1]]*Divide[GegenbauerC[n, \[Lambda], Cos[Subscript[\[Theta], 2]]],GegenbauerC[n, \[Lambda], 1]] == Divide[Gamma[\[Lambda]+Divide[1,2]],(Pi)^(Divide[1,2])* Gamma[\[Lambda]]]* Integrate[Divide[GegenbauerC[n, \[Lambda], Cos[Subscript[\[Theta], 1]]*Cos[Subscript[\[Theta], 2]]+ Sin[Subscript[\[Theta], 1]]*Sin[Subscript[\[Theta], 2]]*Cos[\[Phi]]],GegenbauerC[n, \[Lambda], 1]]*(Sin[\[Phi]])^(2*\[Lambda]- 1), {\[Phi], 0, Pi}, GenerateConditions->None]	Error	Aborted	-	Skipped - Because timed out
18.17.E6	${\displaystyle{\displaystyle P_{n}\left(\cos\theta_{1}\right)P_{n}\left(\cos\theta_{2}\right)=\frac{1}{\pi}\int_{0}^{\pi}P_{n}\left(\cos\theta_{1}\cos\theta_{2}+\sin\theta_{1}\sin\theta_{2}\cos\phi\right)\mathrm{d}\phi}}$ \LegendrepolyP{n}@{\cos@@{\theta_{1}}}\LegendrepolyP{n}@{\cos@@{\theta_{2}}} = \frac{1}{\pi}\int_{0}^{\pi}\LegendrepolyP{n}@{\cos@@{\theta_{1}}\cos@@{\theta_{2}}+\sin@@{\theta_{1}}\sin@@{\theta_{2}}\cos@@{\phi}}\diff{\phi}		LegendreP(n, cos(theta[1]))*LegendreP(n, cos(theta[2])) = (1)/(Pi)*int(LegendreP(n, cos(theta[1])*cos(theta[2])+ sin(theta[1])*sin(theta[2])*cos(phi)), phi = 0..Pi)	LegendreP[n, Cos[Subscript[\[Theta], 1]]]*LegendreP[n, Cos[Subscript[\[Theta], 2]]] == Divide[1,Pi]*Integrate[LegendreP[n, Cos[Subscript[\[Theta], 1]]*Cos[Subscript[\[Theta], 2]]+ Sin[Subscript[\[Theta], 1]]*Sin[Subscript[\[Theta], 2]]*Cos[\[Phi]]], {\[Phi], 0, Pi}, GenerateConditions->None]	Failure	Failure	Successful [Tested: 300]	Successful [Tested: 300]
18.17.E7	${\displaystyle{\displaystyle\left(P_{n}\left(x\right)\right)^{2}+4\pi^{-2}\left(\mathsf{Q}_{n}\left(x\right)\right)^{2}=4\pi^{-2}\*\int_{1}^{\infty}Q_{n}\left(x^{2}+(1-x^{2})t\right)(t^{2}-1)^{-\frac{1}{2}}\mathrm{d}t}}$ \left(\LegendrepolyP{n}@{x}\right)^{2}+4\pi^{-2}\left(\FerrersQ[]{n}@{x}\right)^{2} = 4\pi^{-2}\*\int_{1}^{\infty}\assLegendreQ[]{n}@{x^{2}+(1-x^{2})t}(t^{2}-1)^{-\frac{1}{2}}\diff{t}	${\displaystyle{\displaystyle-1<x,x<1}}$	(LegendreP(n, x))^(2)+ 4*(Pi)^(- 2)*(LegendreQ(n, x))^(2) = 4*(Pi)^(- 2)* int(LegendreQ(n, (x)^(2)+(1 - (x)^(2))*t)*((t)^(2)- 1)^(-(1)/(2)), t = 1..infinity)	(LegendreP[n, x])^(2)+ 4*(Pi)^(- 2)*(LegendreQ[n, x])^(2) == 4*(Pi)^(- 2)* Integrate[LegendreQ[n, 0, 3, (x)^(2)+(1 - (x)^(2))*t]*((t)^(2)- 1)^(-Divide[1,2]), {t, 1, Infinity}, GenerateConditions->None]	Failure	Failure	Failed [3 / 3] Result: 0.+Float(infinity)*I Test Values: {x = 1/2, n = 1} Result: 0.+Float(infinity)*I Test Values: {x = 1/2, n = 2} ... skip entries to safe data	Successful [Tested: 3]
18.17.E8	${\displaystyle{\displaystyle\left(H_{n}\left(x\right)\right)^{2}+2^{n}(n!)^{2}e^{x^{2}}\left(V\left(-n-\tfrac{1}{2},2^{\frac{1}{2}}x\right)\right)^{2}=\frac{2^{n+\frac{3}{2}}n!\,e^{x^{2}}}{\pi}\int_{0}^{\infty}\frac{e^{-(2n+1)t+x^{2}\tanh t}}{(\sinh 2t)^{\frac{1}{2}}}\mathrm{d}t}}$ \left(\HermitepolyH{n}@{x}\right)^{2}+2^{n}(n!)^{2}e^{x^{2}}\left(\paraV@{-n-\tfrac{1}{2}}{2^{\frac{1}{2}}x}\right)^{2} = \frac{2^{n+\frac{3}{2}}n!\,e^{x^{2}}}{\pi}\int_{0}^{\infty}\frac{e^{-(2n+1)t+x^{2}\tanh@@{t}}}{(\sinh@@{2t})^{\frac{1}{2}}}\diff{t}		(HermiteH(n, x))^(2)+ (2)^(n)*(factorial(n))^(2)* exp((x)^(2))*(CylinderV(- n -(1)/(2), (2)^((1)/(2))* x))^(2) = ((2)^(n +(3)/(2))* factorial(n)*exp((x)^(2)))/(Pi)*int((exp(-(2*n + 1)*t + (x)^(2)* tanh(t)))/((sinh(2*t))^((1)/(2))), t = 0..infinity)	(HermiteH[n, x])^(2)+ (2)^(n)*((n)!)^(2)* Exp[(x)^(2)]*(Divide[GAMMA[1/2 + - n -Divide[1,2]], Pi]*(Sin[Pi*(- n -Divide[1,2])] * ParabolicCylinderD[-(- n -Divide[1,2]) - 1/2, (2)^(Divide[1,2])* x] + ParabolicCylinderD[-(- n -Divide[1,2]) - 1/2, -((2)^(Divide[1,2])* x)]))^(2) == Divide[(2)^(n +Divide[3,2])* (n)!*Exp[(x)^(2)],Pi]*Integrate[Divide[Exp[-(2*n + 1)*t + (x)^(2)* Tanh[t]],(Sinh[2*t])^(Divide[1,2])], {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Successful [Tested: 9]	Skipped - Because timed out
18.17.E9	${\displaystyle{\displaystyle\frac{(1-x)^{\alpha+\mu}P^{(\alpha+\mu,\beta-\mu)}_{n}\left(x\right)}{\Gamma\left(\alpha+\mu+n+1\right)}=\int_{x}^{1}\frac{(1-y)^{\alpha}P^{(\alpha,\beta)}_{n}\left(y\right)}{\Gamma\left(\alpha+n+1\right)}\frac{(y-x)^{\mu-1}}{\Gamma\left(\mu\right)}\mathrm{d}y}}$ \frac{(1-x)^{\alpha+\mu}\JacobipolyP{\alpha+\mu}{\beta-\mu}{n}@{x}}{\EulerGamma@{\alpha+\mu+n+1}} = \int_{x}^{1}\frac{(1-y)^{\alpha}\JacobipolyP{\alpha}{\beta}{n}@{y}}{\EulerGamma@{\alpha+n+1}}\frac{(y-x)^{\mu-1}}{\EulerGamma@{\mu}}\diff{y}	${\displaystyle{\displaystyle\mu>0,-1<x,x<1,\Re(\alpha+\mu+n+1)>0,\Re(\alpha+n+1)>0,\Re(\mu)>0}}$	((1 - x)^(alpha + mu)* JacobiP(n, alpha + mu, beta - mu, x))/(GAMMA(alpha + mu + n + 1)) = int(((1 - y)^(alpha)* JacobiP(n, alpha, beta, y))/(GAMMA(alpha + n + 1))*((y - x)^(mu - 1))/(GAMMA(mu)), y = x..1)	Divide[(1 - x)^(\[Alpha]+ \[Mu])* JacobiP[n, \[Alpha]+ \[Mu], \[Beta]- \[Mu], x],Gamma[\[Alpha]+ \[Mu]+ n + 1]] == Integrate[Divide[(1 - y)^\[Alpha]* JacobiP[n, \[Alpha], \[Beta], y],Gamma[\[Alpha]+ n + 1]]*Divide[(y - x)^(\[Mu]- 1),Gamma[\[Mu]]], {y, x, 1}, GenerateConditions->None]	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out
18.17.E10	${\displaystyle{\displaystyle\frac{x^{\beta+\mu}(x+1)^{n}}{\Gamma\left(\beta+\mu+n+1\right)}P^{(\alpha,\beta+\mu)}_{n}\left(\frac{x-1}{x+1}\right)=\int_{0}^{x}\frac{y^{\beta}(y+1)^{n}}{\Gamma\left(\beta+n+1\right)}P^{(\alpha,\beta)}_{n}\left(\frac{y-1}{y+1}\right)\*\frac{(x-y)^{\mu-1}}{\Gamma\left(\mu\right)}\mathrm{d}y}}$ \frac{x^{\beta+\mu}(x+1)^{n}}{\EulerGamma@{\beta+\mu+n+1}}\JacobipolyP{\alpha}{\beta+\mu}{n}@{\frac{x-1}{x+1}} = \int_{0}^{x}\frac{y^{\beta}(y+1)^{n}}{\EulerGamma@{\beta+n+1}}\JacobipolyP{\alpha}{\beta}{n}@{\frac{y-1}{y+1}}\*\frac{(x-y)^{\mu-1}}{\EulerGamma@{\mu}}\diff{y}	${\displaystyle{\displaystyle\mu>0,x>0,\Re(\beta+\mu+n+1)>0,\Re(\beta+n+1)>0,\Re(\mu)>0}}$	((x)^(beta + mu)*(x + 1)^(n))/(GAMMA(beta + mu + n + 1))*JacobiP(n, alpha, beta + mu, (x - 1)/(x + 1)) = int(((y)^(beta)*(y + 1)^(n))/(GAMMA(beta + n + 1))*JacobiP(n, alpha, beta, (y - 1)/(y + 1))*((x - y)^(mu - 1))/(GAMMA(mu)), y = 0..x)	Divide[(x)^(\[Beta]+ \[Mu])*(x + 1)^(n),Gamma[\[Beta]+ \[Mu]+ n + 1]]*JacobiP[n, \[Alpha], \[Beta]+ \[Mu], Divide[x - 1,x + 1]] == Integrate[Divide[(y)^\[Beta]*(y + 1)^(n),Gamma[\[Beta]+ n + 1]]*JacobiP[n, \[Alpha], \[Beta], Divide[y - 1,y + 1]]*Divide[(x - y)^(\[Mu]- 1),Gamma[\[Mu]]], {y, 0, x}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
18.17.E11	${\displaystyle{\displaystyle\frac{\Gamma\left(n+\alpha+\beta-\mu+1\right)}{x^{n+\alpha+\beta-\mu+1}}P^{(\alpha,\beta-\mu)}_{n}\left(1-2x^{-1}\right)=\int_{x}^{\infty}\frac{\Gamma\left(n+\alpha+\beta+1\right)}{y^{n+\alpha+\beta+1}}P^{(\alpha,\beta)}_{n}\left(1-2y^{-1}\right)\*\frac{(y-x)^{\mu-1}}{\Gamma\left(\mu\right)}\mathrm{d}y}}$ \frac{\EulerGamma@{n+\alpha+\beta-\mu+1}}{x^{n+\alpha+\beta-\mu+1}}\JacobipolyP{\alpha}{\beta-\mu}{n}@{1-2x^{-1}} = \int_{x}^{\infty}\frac{\EulerGamma@{n+\alpha+\beta+1}}{y^{n+\alpha+\beta+1}}\JacobipolyP{\alpha}{\beta}{n}@{1-2y^{-1}}\*\frac{(y-x)^{\mu-1}}{\EulerGamma@{\mu}}\diff{y}	${\displaystyle{\displaystyle\alpha+\beta+1>\mu,\mu>0,x>1,\Re(n+\alpha+\beta-\mu+1)>0,\Re(n+\alpha+\beta+1)>0,\Re(\mu)>0}}$	(GAMMA(n + alpha + beta - mu + 1))/((x)^(n + alpha + beta - mu + 1))*JacobiP(n, alpha, beta - mu, 1 - 2*(x)^(- 1)) = int((GAMMA(n + alpha + beta + 1))/((y)^(n + alpha + beta + 1))*JacobiP(n, alpha, beta, 1 - 2*(y)^(- 1))*((y - x)^(mu - 1))/(GAMMA(mu)), y = x..infinity)	Divide[Gamma[n + \[Alpha]+ \[Beta]- \[Mu]+ 1],(x)^(n + \[Alpha]+ \[Beta]- \[Mu]+ 1)]*JacobiP[n, \[Alpha], \[Beta]- \[Mu], 1 - 2*(x)^(- 1)] == Integrate[Divide[Gamma[n + \[Alpha]+ \[Beta]+ 1],(y)^(n + \[Alpha]+ \[Beta]+ 1)]*JacobiP[n, \[Alpha], \[Beta], 1 - 2*(y)^(- 1)]*Divide[(y - x)^(\[Mu]- 1),Gamma[\[Mu]]], {y, x, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
18.17.E12	${\displaystyle{\displaystyle\frac{\Gamma\left(\lambda-\mu\right)C^{(\lambda-\mu)}_{n}\left(x^{-\frac{1}{2}}\right)}{x^{\lambda-\mu+\frac{1}{2}n}}=\int_{x}^{\infty}\frac{\Gamma\left(\lambda\right)C^{(\lambda)}_{n}\left(y^{-\frac{1}{2}}\right)}{y^{\lambda+\frac{1}{2}n}}\frac{(y-x)^{\mu-1}}{\Gamma\left(\mu\right)}\mathrm{d}y}}$ \frac{\EulerGamma@{\lambda-\mu}\ultrasphpoly{\lambda-\mu}{n}@{x^{-\frac{1}{2}}}}{x^{\lambda-\mu+\frac{1}{2}n}} = \int_{x}^{\infty}\frac{\EulerGamma@{\lambda}\ultrasphpoly{\lambda}{n}@{y^{-\frac{1}{2}}}}{y^{\lambda+\frac{1}{2}n}}\frac{(y-x)^{\mu-1}}{\EulerGamma@{\mu}}\diff{y}	${\displaystyle{\displaystyle\lambda>\mu,\mu>0,x>0,\Re(\lambda-\mu)>0,\Re(\lambda)>0,\Re(\mu)>0}}$	(GAMMA(lambda - mu)*GegenbauerC(n, lambda - mu, (x)^(-(1)/(2))))/((x)^(lambda - mu +(1)/(2)*n)) = int((GAMMA(lambda)*GegenbauerC(n, lambda, (y)^(-(1)/(2))))/((y)^(lambda +(1)/(2)*n))*((y - x)^(mu - 1))/(GAMMA(mu)), y = x..infinity)	Divide[Gamma[\[Lambda]- \[Mu]]*GegenbauerC[n, \[Lambda]- \[Mu], (x)^(-Divide[1,2])],(x)^(\[Lambda]- \[Mu]+Divide[1,2]*n)] == Integrate[Divide[Gamma[\[Lambda]]*GegenbauerC[n, \[Lambda], (y)^(-Divide[1,2])],(y)^(\[Lambda]+Divide[1,2]*n)]*Divide[(y - x)^(\[Mu]- 1),Gamma[\[Mu]]], {y, x, Infinity}, GenerateConditions->None]	Error	Aborted	-	Skipped - Because timed out
18.17.E13	${\displaystyle{\displaystyle\frac{x^{\frac{1}{2}n}(x-1)^{\lambda+\mu-\frac{1}{2}}}{\Gamma\left(\lambda+\mu+\tfrac{1}{2}\right)}\frac{C^{(\lambda+\mu)}_{n}\left(x^{-\frac{1}{2}}\right)}{C^{(\lambda+\mu)}_{n}\left(1\right)}=\int_{1}^{x}\frac{y^{\frac{1}{2}n}(y-1)^{\lambda-\frac{1}{2}}}{\Gamma\left(\lambda+\tfrac{1}{2}\right)}\frac{C^{(\lambda)}_{n}\left(y^{-\frac{1}{2}}\right)}{C^{(\lambda)}_{n}\left(1\right)}\frac{(x-y)^{\mu-1}}{\Gamma\left(\mu\right)}\mathrm{d}y}}$ \frac{x^{\frac{1}{2}n}(x-1)^{\lambda+\mu-\frac{1}{2}}}{\EulerGamma@{\lambda+\mu+\tfrac{1}{2}}}\frac{\ultrasphpoly{\lambda+\mu}{n}@{x^{-\frac{1}{2}}}}{\ultrasphpoly{\lambda+\mu}{n}@{1}} = \int_{1}^{x}\frac{y^{\frac{1}{2}n}(y-1)^{\lambda-\frac{1}{2}}}{\EulerGamma@{\lambda+\tfrac{1}{2}}}\frac{\ultrasphpoly{\lambda}{n}@{y^{-\frac{1}{2}}}}{\ultrasphpoly{\lambda}{n}@{1}}\frac{(x-y)^{\mu-1}}{\EulerGamma@{\mu}}\diff{y}	${\displaystyle{\displaystyle\mu>0,x>1,\Re(\lambda+\mu+\tfrac{1}{2})>0,\Re(\lambda+\tfrac{1}{2})>0,\Re(\mu)>0}}$	((x)^((1)/(2)*n)*(x - 1)^(lambda + mu -(1)/(2)))/(GAMMA(lambda + mu +(1)/(2)))*(GegenbauerC(n, lambda + mu, (x)^(-(1)/(2))))/(GegenbauerC(n, lambda + mu, 1)) = int(((y)^((1)/(2)*n)*(y - 1)^(lambda -(1)/(2)))/(GAMMA(lambda +(1)/(2)))*(GegenbauerC(n, lambda, (y)^(-(1)/(2))))/(GegenbauerC(n, lambda, 1))*((x - y)^(mu - 1))/(GAMMA(mu)), y = 1..x)	Divide[(x)^(Divide[1,2]*n)*(x - 1)^(\[Lambda]+ \[Mu]-Divide[1,2]),Gamma[\[Lambda]+ \[Mu]+Divide[1,2]]]*Divide[GegenbauerC[n, \[Lambda]+ \[Mu], (x)^(-Divide[1,2])],GegenbauerC[n, \[Lambda]+ \[Mu], 1]] == Integrate[Divide[(y)^(Divide[1,2]*n)*(y - 1)^(\[Lambda]-Divide[1,2]),Gamma[\[Lambda]+Divide[1,2]]]*Divide[GegenbauerC[n, \[Lambda], (y)^(-Divide[1,2])],GegenbauerC[n, \[Lambda], 1]]*Divide[(x - y)^(\[Mu]- 1),Gamma[\[Mu]]], {y, 1, x}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
18.17.E14	${\displaystyle{\displaystyle\frac{x^{\alpha+\mu}L^{(\alpha+\mu)}_{n}\left(x\right)}{\Gamma\left(\alpha+\mu+n+1\right)}=\int_{0}^{x}\frac{y^{\alpha}L^{(\alpha)}_{n}\left(y\right)}{\Gamma\left(\alpha+n+1\right)}\frac{(x-y)^{\mu-1}}{\Gamma\left(\mu\right)}\mathrm{d}y}}$ \frac{x^{\alpha+\mu}\LaguerrepolyL[\alpha+\mu]{n}@{x}}{\EulerGamma@{\alpha+\mu+n+1}} = \int_{0}^{x}\frac{y^{\alpha}\LaguerrepolyL[\alpha]{n}@{y}}{\EulerGamma@{\alpha+n+1}}\frac{(x-y)^{\mu-1}}{\EulerGamma@{\mu}}\diff{y}	${\displaystyle{\displaystyle\mu>0,x>0,\Re(\alpha+\mu+n+1)>0,\Re(\alpha+n+1)>0,\Re(\mu)>0}}$	((x)^(alpha + mu)* LaguerreL(n, alpha + mu, x))/(GAMMA(alpha + mu + n + 1)) = int(((y)^(alpha)* LaguerreL(n, alpha, y))/(GAMMA(alpha + n + 1))*((x - y)^(mu - 1))/(GAMMA(mu)), y = 0..x)	Divide[(x)^(\[Alpha]+ \[Mu])* LaguerreL[n, \[Alpha]+ \[Mu], x],Gamma[\[Alpha]+ \[Mu]+ n + 1]] == Integrate[Divide[(y)^\[Alpha]* LaguerreL[n, \[Alpha], y],Gamma[\[Alpha]+ n + 1]]*Divide[(x - y)^(\[Mu]- 1),Gamma[\[Mu]]], {y, 0, x}, GenerateConditions->None]	Missing Macro Error	Failure	-	Manual Skip!
18.17.E15	${\displaystyle{\displaystyle e^{-x}L^{(\alpha)}_{n}\left(x\right)=\int_{x}^{\infty}e^{-y}L^{(\alpha+\mu)}_{n}\left(y\right)\frac{(y-x)^{\mu-1}}{\Gamma\left(\mu\right)}\mathrm{d}y}}$ e^{-x}\LaguerrepolyL[\alpha]{n}@{x} = \int_{x}^{\infty}e^{-y}\LaguerrepolyL[\alpha+\mu]{n}@{y}\frac{(y-x)^{\mu-1}}{\EulerGamma@{\mu}}\diff{y}	${\displaystyle{\displaystyle\mu>0,\Re(\mu)>0}}$	exp(- x)*LaguerreL(n, alpha, x) = int(exp(- y)*LaguerreL(n, alpha + mu, y)*((y - x)^(mu - 1))/(GAMMA(mu)), y = x..infinity)	Exp[- x]*LaguerreL[n, \[Alpha], x] == Integrate[Exp[- y]*LaguerreL[n, \[Alpha]+ \[Mu], y]*Divide[(y - x)^(\[Mu]- 1),Gamma[\[Mu]]], {y, x, Infinity}, GenerateConditions->None]	Missing Macro Error	Aborted	-	Skipped - Because timed out
18.17.E16	${\displaystyle{\displaystyle\int_{-1}^{1}(1-x)^{\alpha}(1+x)^{\beta}P^{(\alpha,\beta)}_{n}\left(x\right)e^{ixy}\mathrm{d}x=\frac{(iy)^{n}e^{iy}}{n!}2^{n+\alpha+\beta+1}\mathrm{B}\left(n+\alpha+1,n+\beta+1\right){{}_{1}F_{1}}\left(n+\alpha+1;2n+\alpha+\beta+2;-2iy\right)}}$ \int_{-1}^{1}(1-x)^{\alpha}(1+x)^{\beta}\JacobipolyP{\alpha}{\beta}{n}@{x}e^{ixy}\diff{x} = \frac{(iy)^{n}e^{iy}}{n!}2^{n+\alpha+\beta+1}\EulerBeta@{n+\alpha+1}{n+\beta+1}\genhyperF{1}{1}@{n+\alpha+1}{2n+\alpha+\beta+2}{-2iy}	${\displaystyle{\displaystyle\Re(n+\alpha+1)>0,\Re(n+\beta+1)>0,\Re((n+\alpha+1)+b)>0,\Re(a+(n+\beta+1))>0}}$	int((1 - x)^(alpha)*(1 + x)^(beta)* JacobiP(n, alpha, beta, x)*exp(I*x*y), x = - 1..1) = ((I*y)^(n)* exp(I*y))/(factorial(n))*(2)^(n + alpha + beta + 1)* Beta(n + alpha + 1, n + beta + 1)*hypergeom([n + alpha + 1], [2*n + alpha + beta + 2], - 2*I*y)	Integrate[(1 - x)^\[Alpha]*(1 + x)^\[Beta]* JacobiP[n, \[Alpha], \[Beta], x]*Exp[I*x*y], {x, - 1, 1}, GenerateConditions->None] == Divide[(I*y)^(n)* Exp[I*y],(n)!]*(2)^(n + \[Alpha]+ \[Beta]+ 1)* Beta[n + \[Alpha]+ 1, n + \[Beta]+ 1]*HypergeometricPFQ[{n + \[Alpha]+ 1}, {2*n + \[Alpha]+ \[Beta]+ 2}, - 2*I*y]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
18.17.E17	${\displaystyle{\displaystyle\int_{0}^{1}(1-x^{2})^{\lambda-\frac{1}{2}}C^{(\lambda)}_{2n}\left(x\right)\cos\left(xy\right)\mathrm{d}x=\frac{(-1)^{n}\pi\Gamma\left(2n+2\lambda\right)J_{\lambda+2n}\left(y\right)}{(2n)!\Gamma\left(\lambda\right)(2y)^{\lambda}}}}$ \int_{0}^{1}(1-x^{2})^{\lambda-\frac{1}{2}}\ultrasphpoly{\lambda}{2n}@{x}\cos@{xy}\diff{x} = \frac{(-1)^{n}\pi\EulerGamma@{2n+2\lambda}\BesselJ{\lambda+2n}@{y}}{(2n)!\EulerGamma@{\lambda}(2y)^{\lambda}}	${\displaystyle{\displaystyle\Re((\lambda+2n)+k+1)>0,\Re(2n+2\lambda)>0,\Re(\lambda)>0}}$	int((1 - (x)^(2))^(lambda -(1)/(2))* GegenbauerC(2*n, lambda, x)*cos(x*y), x = 0..1) = ((- 1)^(n)* Pi*GAMMA(2*n + 2*lambda)*BesselJ(lambda + 2*n, y))/(factorial(2*n)*GAMMA(lambda)*(2*y)^(lambda))	Integrate[(1 - (x)^(2))^(\[Lambda]-Divide[1,2])* GegenbauerC[2*n, \[Lambda], x]*Cos[x*y], {x, 0, 1}, GenerateConditions->None] == Divide[(- 1)^(n)* Pi*Gamma[2*n + 2*\[Lambda]]*BesselJ[\[Lambda]+ 2*n, y],(2*n)!*Gamma[\[Lambda]]*(2*y)^\[Lambda]]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
18.17.E18	${\displaystyle{\displaystyle\int_{0}^{1}(1-x^{2})^{\lambda-\frac{1}{2}}C^{(\lambda)}_{2n+1}\left(x\right)\sin\left(xy\right)\mathrm{d}x=\frac{(-1)^{n}\pi\Gamma\left(2n+2\lambda+1\right)J_{2n+\lambda+1}\left(y\right)}{(2n+1)!\Gamma\left(\lambda\right)(2y)^{\lambda}}}}$ \int_{0}^{1}(1-x^{2})^{\lambda-\frac{1}{2}}\ultrasphpoly{\lambda}{2n+1}@{x}\sin@{xy}\diff{x} = \frac{(-1)^{n}\pi\EulerGamma@{2n+2\lambda+1}\BesselJ{2n+\lambda+1}@{y}}{(2n+1)!\EulerGamma@{\lambda}(2y)^{\lambda}}	${\displaystyle{\displaystyle\Re((2n+\lambda+1)+k+1)>0,\Re(2n+2\lambda+1)>0,\Re(\lambda)>0}}$	int((1 - (x)^(2))^(lambda -(1)/(2))* GegenbauerC(2*n + 1, lambda, x)*sin(x*y), x = 0..1) = ((- 1)^(n)* Pi*GAMMA(2*n + 2*lambda + 1)*BesselJ(2*n + lambda + 1, y))/(factorial(2*n + 1)*GAMMA(lambda)*(2*y)^(lambda))	Integrate[(1 - (x)^(2))^(\[Lambda]-Divide[1,2])* GegenbauerC[2*n + 1, \[Lambda], x]*Sin[x*y], {x, 0, 1}, GenerateConditions->None] == Divide[(- 1)^(n)* Pi*Gamma[2*n + 2*\[Lambda]+ 1]*BesselJ[2*n + \[Lambda]+ 1, y],(2*n + 1)!*Gamma[\[Lambda]]*(2*y)^\[Lambda]]	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out
18.17.E19	${\displaystyle{\displaystyle\int_{-1}^{1}P_{n}\left(x\right)e^{ixy}\mathrm{d}x=i^{n}\sqrt{\frac{2\pi}{y}}J_{n+\frac{1}{2}}\left(y\right)}}$ \int_{-1}^{1}\LegendrepolyP{n}@{x}e^{ixy}\diff{x} = i^{n}\sqrt{\frac{2\pi}{y}}\BesselJ{n+\frac{1}{2}}@{y}	${\displaystyle{\displaystyle\Re((n+\frac{1}{2})+k+1)>0}}$	int(LegendreP(n, x)*exp(I*x*y), x = - 1..1) = (I)^(n)*sqrt((2*Pi)/(y))*BesselJ(n +(1)/(2), y)	Integrate[LegendreP[n, x]*Exp[I*x*y], {x, - 1, 1}, GenerateConditions->None] == (I)^(n)*Sqrt[Divide[2*Pi,y]]*BesselJ[n +Divide[1,2], y]	Failure	Failure	Failed [9 / 18] Result: -.1455515881e-15-1.584691883*I Test Values: {y = -3/2, n = 1} Result: -.5093971348+.7797894631e-16*I Test Values: {y = -3/2, n = 2} ... skip entries to safe data	Failed [9 / 18] Result: Complex[0.0, -1.584691882848889] Test Values: {Rule[n, 1], Rule[y, -1.5]} Result: Complex[-0.5093971347536326, -3.3306690738754696*^-16] Test Values: {Rule[n, 2], Rule[y, -1.5]} ... skip entries to safe data
18.17.E20	${\displaystyle{\displaystyle\int_{0}^{1}P_{n}\left(1-2x^{2}\right)\cos\left(xy\right)\mathrm{d}x=(-1)^{n}\tfrac{1}{2}\pi J_{n+\frac{1}{2}}\left(\tfrac{1}{2}y\right)J_{-n-\frac{1}{2}}\left(\tfrac{1}{2}y\right)}}$ \int_{0}^{1}\LegendrepolyP{n}@{1-2x^{2}}\cos@{xy}\diff{x} = (-1)^{n}\tfrac{1}{2}\pi\BesselJ{n+\frac{1}{2}}@{\tfrac{1}{2}y}\BesselJ{-n-\frac{1}{2}}@{\tfrac{1}{2}y}	${\displaystyle{\displaystyle\Re((n+\frac{1}{2})+k+1)>0,\Re((-n-\frac{1}{2})+k+1)>0}}$	int(LegendreP(n, 1 - 2*(x)^(2))*cos(x*y), x = 0..1) = (- 1)^(n)*(1)/(2)*Pi*BesselJ(n +(1)/(2), (1)/(2)*y)*BesselJ(- n -(1)/(2), (1)/(2)*y)	Integrate[LegendreP[n, 1 - 2*(x)^(2)]*Cos[x*y], {x, 0, 1}, GenerateConditions->None] == (- 1)^(n)*Divide[1,2]*Pi*BesselJ[n +Divide[1,2], Divide[1,2]*y]*BesselJ[- n -Divide[1,2], Divide[1,2]*y]	Failure	Failure	Successful [Tested: 18]	Successful [Tested: 18]
18.17.E21	${\displaystyle{\displaystyle\int_{0}^{1}P_{n}\left(1-2x^{2}\right)\sin\left(xy\right)\mathrm{d}x=\tfrac{1}{2}\pi\left(J_{n+\frac{1}{2}}\left(\tfrac{1}{2}y\right)\right)^{2}}}$ \int_{0}^{1}\LegendrepolyP{n}@{1-2x^{2}}\sin@{xy}\diff{x} = \tfrac{1}{2}\pi\left(\BesselJ{n+\frac{1}{2}}@{\tfrac{1}{2}y}\right)^{2}	${\displaystyle{\displaystyle\Re((n+\frac{1}{2})+k+1)>0}}$	int(LegendreP(n, 1 - 2*(x)^(2))*sin(x*y), x = 0..1) = (1)/(2)*Pi*(BesselJ(n +(1)/(2), (1)/(2)*y))^(2)	Integrate[LegendreP[n, 1 - 2*(x)^(2)]*Sin[x*y], {x, 0, 1}, GenerateConditions->None] == Divide[1,2]*Pi*(BesselJ[n +Divide[1,2], Divide[1,2]*y])^(2)	Failure	Failure	Successful [Tested: 18]	Successful [Tested: 18]
18.17.E30	${\displaystyle{\displaystyle\int_{0}^{\infty}x^{2n}e^{-\frac{1}{2}x^{2}}L^{(n-\frac{1}{2})}_{n}\left(\tfrac{1}{2}x^{2}\right)\cos\left(xy\right)\mathrm{d}x=\sqrt{\tfrac{1}{2}\pi}y^{2n}e^{-\frac{1}{2}y^{2}}L^{(n-\frac{1}{2})}_{n}\left(\tfrac{1}{2}y^{2}\right)}}$ \int_{0}^{\infty}x^{2n}e^{-\frac{1}{2}x^{2}}\LaguerrepolyL[n-\frac{1}{2}]{n}@{\tfrac{1}{2}x^{2}}\cos@{xy}\diff{x} = \sqrt{\tfrac{1}{2}\pi}y^{2n}e^{-\frac{1}{2}y^{2}}\LaguerrepolyL[n-\frac{1}{2}]{n}@{\tfrac{1}{2}y^{2}}		int((x)^(2*n)* exp(-(1)/(2)*(x)^(2))*LaguerreL(n, n -(1)/(2), (1)/(2)*(x)^(2))*cos(x*y), x = 0..infinity) = sqrt((1)/(2)*Pi)*(y)^(2*n)* exp(-(1)/(2)*(y)^(2))*LaguerreL(n, n -(1)/(2), (1)/(2)*(y)^(2))	Integrate[(x)^(2*n)* Exp[-Divide[1,2]*(x)^(2)]*LaguerreL[n, n -Divide[1,2], Divide[1,2]*(x)^(2)]*Cos[x*y], {x, 0, Infinity}, GenerateConditions->None] == Sqrt[Divide[1,2]*Pi]*(y)^(2*n)* Exp[-Divide[1,2]*(y)^(2)]*LaguerreL[n, n -Divide[1,2], Divide[1,2]*(y)^(2)]	Missing Macro Error	Aborted	-	Skipped - Because timed out
18.17.E31	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-ax}x^{\nu-2n}L^{(\nu-2n)}_{2n-1}\left(ax\right)\cos\left(xy\right)\mathrm{d}x=i\frac{(-1)^{n}\Gamma\left(\nu\right)}{2(2n-1)!}y^{2n-1}\left((a+iy)^{-\nu}-(a-iy)^{-\nu}\right)}}$ \int_{0}^{\infty}e^{-ax}x^{\nu-2n}\LaguerrepolyL[\nu-2n]{2n-1}@{ax}\cos@{xy}\diff{x} = i\frac{(-1)^{n}\EulerGamma@{\nu}}{2(2n-1)!}y^{2n-1}\left((a+iy)^{-\nu}-(a-iy)^{-\nu}\right)	${\displaystyle{\displaystyle\nu>2n-1,a>0,\Re(\nu)>0}}$	int(exp(- a*x)*(x)^(nu - 2*n)* LaguerreL(2*n - 1, nu - 2*n, a*x)*cos(x*y), x = 0..infinity) = I*((- 1)^(n)* GAMMA(nu))/(2*factorial(2*n - 1))*(y)^(2*n - 1)*((a + I*y)^(- nu)-(a - I*y)^(- nu))	Integrate[Exp[- a*x]*(x)^(\[Nu]- 2*n)* LaguerreL[2*n - 1, \[Nu]- 2*n, a*x]*Cos[x*y], {x, 0, Infinity}, GenerateConditions->None] == I*Divide[(- 1)^(n)* Gamma[\[Nu]],2*(2*n - 1)!]*(y)^(2*n - 1)*((a + I*y)^(- \[Nu])-(a - I*y)^(- \[Nu]))	Missing Macro Error	Aborted	-	Skipped - Because timed out
18.17.E32	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-ax}x^{\nu-1-2n}L^{(\nu-1-2n)}_{2n}\left(ax\right)\cos\left(xy\right)\mathrm{d}x=\frac{(-1)^{n}\Gamma\left(\nu\right)}{2(2n)!}y^{2n}\left((a+iy)^{-\nu}+(a-iy)^{-\nu}\right)}}$ \int_{0}^{\infty}e^{-ax}x^{\nu-1-2n}\LaguerrepolyL[\nu-1-2n]{2n}@{ax}\cos@{xy}\diff{x} = \frac{(-1)^{n}\EulerGamma@{\nu}}{2(2n)!}y^{2n}\left((a+iy)^{-\nu}+(a-iy)^{-\nu}\right)	${\displaystyle{\displaystyle\nu>2n,a>0,\Re(\nu)>0}}$	int(exp(- a*x)*(x)^(nu - 1 - 2*n)* LaguerreL(2*n, nu - 1 - 2*n, a*x)*cos(x*y), x = 0..infinity) = ((- 1)^(n)* GAMMA(nu))/(2*factorial(2*n))*(y)^(2*n)*((a + I*y)^(- nu)+(a - I*y)^(- nu))	Integrate[Exp[- a*x]*(x)^(\[Nu]- 1 - 2*n)* LaguerreL[2*n, \[Nu]- 1 - 2*n, a*x]*Cos[x*y], {x, 0, Infinity}, GenerateConditions->None] == Divide[(- 1)^(n)* Gamma[\[Nu]],2*(2*n)!]*(y)^(2*n)*((a + I*y)^(- \[Nu])+(a - I*y)^(- \[Nu]))	Missing Macro Error	Aborted	-	Skipped - Because timed out
18.17.E33	${\displaystyle{\displaystyle\int_{-1}^{1}e^{-(x+1)z}P^{(\alpha,\beta)}_{n}\left(x\right)(1-x)^{\alpha}(1+x)^{\beta}\mathrm{d}x=\frac{(-1)^{n}2^{\alpha+\beta+n+1}\Gamma\left(\alpha+n+1\right)\Gamma\left(\beta+n+1\right)}{\Gamma\left(\alpha+\beta+2n+2\right)n!}z^{n}{{}_{1}F_{1}}\left({\beta+n+1\atop\alpha+\beta+2n+2};-2z\right)}}$ \int_{-1}^{1}e^{-(x+1)z}\JacobipolyP{\alpha}{\beta}{n}@{x}(1-x)^{\alpha}(1+x)^{\beta}\diff{x} = \frac{(-1)^{n}2^{\alpha+\beta+n+1}\EulerGamma@{\alpha+n+1}\EulerGamma@{\beta+n+1}}{\EulerGamma@{\alpha+\beta+2n+2}n!}z^{n}\genhyperF{1}{1}@@{\beta+n+1}{\alpha+\beta+2n+2}{-2z}	${\displaystyle{\displaystyle\Re(\alpha+n+1)>0,\Re(\beta+n+1)>0,\Re(\alpha+\beta+2n+2)>0}}$	int(exp(-(x + 1)*(x + y*I))*JacobiP(n, alpha, beta, x)*(1 - x)^(alpha)*(1 + x)^(beta), x = - 1..1) = ((- 1)^(n)* (2)^(alpha + beta + n + 1)* GAMMA(alpha + n + 1)*GAMMA(beta + n + 1))/(GAMMA(alpha + beta + 2*n + 2)*factorial(n))*(x + y*I)^(n)* hypergeom([beta + n + 1], [alpha + beta + 2*n + 2], - 2*(x + y*I))	Integrate[Exp[-(x + 1)*(x + y*I)]*JacobiP[n, \[Alpha], \[Beta], x]*(1 - x)^\[Alpha]*(1 + x)^\[Beta], {x, - 1, 1}, GenerateConditions->None] == Divide[(- 1)^(n)* (2)^(\[Alpha]+ \[Beta]+ n + 1)* Gamma[\[Alpha]+ n + 1]*Gamma[\[Beta]+ n + 1],Gamma[\[Alpha]+ \[Beta]+ 2*n + 2]*(n)!]*(x + y*I)^(n)* HypergeometricPFQ[{\[Beta]+ n + 1}, {\[Alpha]+ \[Beta]+ 2*n + 2}, - 2*(x + y*I)]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
18.17.E34	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-xz}L^{(\alpha)}_{n}\left(x\right)e^{-x}x^{\alpha}\mathrm{d}x=\frac{\Gamma\left(\alpha+n+1\right)z^{n}}{n!(z+1)^{\alpha+n+1}}}}$ \int_{0}^{\infty}e^{-xz}\LaguerrepolyL[\alpha]{n}@{x}e^{-x}x^{\alpha}\diff{x} = \frac{\EulerGamma@{\alpha+n+1}z^{n}}{n!(z+1)^{\alpha+n+1}}	${\displaystyle{\displaystyle\Re z>-1,\Re(\alpha+n+1)>0}}$	int(exp(- x*(x + y*I))*LaguerreL(n, alpha, x)*exp(- x)*(x)^(alpha), x = 0..infinity) = (GAMMA(alpha + n + 1)*(x + y*I)^(n))/(factorial(n)*((x + y*I)+ 1)^(alpha + n + 1))	Integrate[Exp[- x*(x + y*I)]*LaguerreL[n, \[Alpha], x]*Exp[- x]*(x)^\[Alpha], {x, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[\[Alpha]+ n + 1]*(x + y*I)^(n),(n)!*((x + y*I)+ 1)^(\[Alpha]+ n + 1)]	Missing Macro Error	Failure	-	Failed [162 / 162] Result: Plus[Complex[-0.07467065623203636, -0.1489394690482153], NIntegrate[Complex[-0.027140152128725715, 0.033616541935162864] Test Values: {1.5, 0, DirectedInfinity[1]}]], {Rule[n, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5]} Result: Plus[Complex[-0.13823623490446432, -0.16092399439966643], NIntegrate[Complex[-0.006785038032181429, 0.008404135483790716] Test Values: {1.5, 0, DirectedInfinity[1]}]], {Rule[n, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5]} ... skip entries to safe data
18.17.E35	${\displaystyle{\displaystyle\int_{-\infty}^{\infty}e^{-xz}H_{n}\left(x\right)e^{-x^{2}}\mathrm{d}x=\pi^{\frac{1}{2}}(-z)^{n}e^{\frac{1}{4}z^{2}}}}$ \int_{-\infty}^{\infty}e^{-xz}\HermitepolyH{n}@{x}e^{-x^{2}}\diff{x} = \pi^{\frac{1}{2}}(-z)^{n}e^{\frac{1}{4}z^{2}}		int(exp(- x*(x + y*I))*HermiteH(n, x)*exp(- (x)^(2)), x = - infinity..infinity) = (Pi)^((1)/(2))*(-(x + y*I))^(n)* exp((1)/(4)*(x + y*I)^(2))	Integrate[Exp[- x*(x + y*I)]*HermiteH[n, x]*Exp[- (x)^(2)], {x, - Infinity, Infinity}, GenerateConditions->None] == (Pi)^(Divide[1,2])*(-(x + y*I))^(n)* Exp[Divide[1,4]*(x + y*I)^(2)]	Failure	Failure	Failed [54 / 54] Result: -1.252480791-2.835663866*I Test Values: {x = 3/2, y = -3/2, n = 1, z = 1+I} Result: 5.718319609+3.439082150*I Test Values: {x = 3/2, y = -3/2, n = 2, z = 1+I} ... skip entries to safe data	Failed [54 / 54] Result: Plus[Complex[-1.25248079113256, -3.5452022239920282], NIntegrate[Complex[-0.020935135800726114, 0.025930837352181123] Test Values: {1.5, DirectedInfinity[-1], DirectedInfinity[1]}]], {Rule[n, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[z, Complex[1, 1]]} Result: Plus[Complex[7.196524522686883, 3.4390821492892023], NIntegrate[Complex[-0.048848650201694266, 0.060505287155089287] Test Values: {1.5, DirectedInfinity[-1], DirectedInfinity[1]}]], {Rule[n, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[z, Complex[1, 1]]} ... skip entries to safe data
18.17.E36	${\displaystyle{\displaystyle\int_{-1}^{1}(1-x)^{z-1}(1+x)^{\beta}P^{(\alpha,\beta)}_{n}\left(x\right)\mathrm{d}x=\frac{2^{\beta+z}\Gamma\left(z\right)\Gamma\left(1+\beta+n\right){\left(1+\alpha-z\right)_{n}}}{n!\Gamma\left(1+\beta+z+n\right)}}}$ \int_{-1}^{1}(1-x)^{z-1}(1+x)^{\beta}\JacobipolyP{\alpha}{\beta}{n}@{x}\diff{x} = \frac{2^{\beta+z}\EulerGamma@{z}\EulerGamma@{1+\beta+n}\Pochhammersym{1+\alpha-z}{n}}{n!\EulerGamma@{1+\beta+z+n}}	${\displaystyle{\displaystyle\Re z>0,\Re(1+\beta+n)>0,\Re(1+\beta+z+n)>0}}$	int((1 - x)^((x + y*I)- 1)*(1 + x)^(beta)* JacobiP(n, alpha, beta, x), x = - 1..1) = ((2)^(beta +(x + y*I))* GAMMA(x + y*I)*GAMMA(1 + beta + n)*pochhammer(1 + alpha -(x + y*I), n))/(factorial(n)*GAMMA(1 + beta +(x + y*I)+ n))	Integrate[(1 - x)^((x + y*I)- 1)*(1 + x)^\[Beta]* JacobiP[n, \[Alpha], \[Beta], x], {x, - 1, 1}, GenerateConditions->None] == Divide[(2)^(\[Beta]+(x + y*I))* Gamma[x + y*I]*Gamma[1 + \[Beta]+ n]*Pochhammer[1 + \[Alpha]-(x + y*I), n],(n)!*Gamma[1 + \[Beta]+(x + y*I)+ n]]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
18.17.E37	${\displaystyle{\displaystyle\int_{0}^{1}(1-x^{2})^{\lambda-\frac{1}{2}}C^{(\lambda)}_{n}\left(x\right)x^{z-1}\mathrm{d}x=\frac{\pi\,2^{1-2\lambda-z}\Gamma\left(n+2\lambda\right)\Gamma\left(z\right)}{n!\Gamma\left(\lambda\right)\Gamma\left(\frac{1}{2}+\frac{1}{2}n+\lambda+\frac{1}{2}z\right)\Gamma\left(\frac{1}{2}+\frac{1}{2}z-\frac{1}{2}n\right)}}}$ \int_{0}^{1}(1-x^{2})^{\lambda-\frac{1}{2}}\ultrasphpoly{\lambda}{n}@{x}x^{z-1}\diff{x} = \frac{\pi\,2^{1-2\lambda-z}\EulerGamma@{n+2\lambda}\EulerGamma@{z}}{n!\EulerGamma@{\lambda}\EulerGamma@{\frac{1}{2}+\frac{1}{2}n+\lambda+\frac{1}{2}z}\EulerGamma@{\frac{1}{2}+\frac{1}{2}z-\frac{1}{2}n}}	${\displaystyle{\displaystyle\Re z>0,\Re(n+2\lambda)>0,\Re(\lambda)>0,\Re(\frac{1}{2}+\frac{1}{2}n+\lambda+\frac{1}{2}z)>0,\Re(\frac{1}{2}+\frac{1}{2}z-\frac{1}{2}n)>0}}$	int((1 - (x)^(2))^(lambda -(1)/(2))* GegenbauerC(n, lambda, x)*(x)^((x + y*I)- 1), x = 0..1) = (Pi*(2)^(1 - 2*lambda -(x + y*I))* GAMMA(n + 2*lambda)*GAMMA(x + y*I))/(factorial(n)*GAMMA(lambda)*GAMMA((1)/(2)+(1)/(2)*n + lambda +(1)/(2)*(x + y*I))*GAMMA((1)/(2)+(1)/(2)*(x + y*I)-(1)/(2)*n))	Integrate[(1 - (x)^(2))^(\[Lambda]-Divide[1,2])* GegenbauerC[n, \[Lambda], x]*(x)^((x + y*I)- 1), {x, 0, 1}, GenerateConditions->None] == Divide[Pi*(2)^(1 - 2*\[Lambda]-(x + y*I))* Gamma[n + 2*\[Lambda]]*Gamma[x + y*I],(n)!*Gamma[\[Lambda]]*Gamma[Divide[1,2]+Divide[1,2]*n + \[Lambda]+Divide[1,2]*(x + y*I)]*Gamma[Divide[1,2]+Divide[1,2]*(x + y*I)-Divide[1,2]*n]]	Failure	Aborted	Skipped - Because timed out	Failed [270 / 270] Result: Plus[Complex[-0.2612561594092788, -0.2567131462958256], NIntegrate[Complex[0.3181035727957409, 0.7653241874975689] Test Values: {1.5, 0, 1}]], {Rule[n, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Plus[Complex[-0.264978322932814, -0.1130252321165333], NIntegrate[Complex[0.21035635691874377, 2.1256411810993385] Test Values: {1.5, 0, 1}]], {Rule[n, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.17.E38	${\displaystyle{\displaystyle\int_{0}^{1}P_{2n}\left(x\right)x^{z-1}\mathrm{d}x=\frac{(-1)^{n}{\left(\frac{1}{2}-\frac{1}{2}z\right)_{n}}}{2{\left(\frac{1}{2}z\right)_{n+1}}}}}$ \int_{0}^{1}\LegendrepolyP{2n}@{x}x^{z-1}\diff{x} = \frac{(-1)^{n}\Pochhammersym{\frac{1}{2}-\frac{1}{2}z}{n}}{2\Pochhammersym{\frac{1}{2}z}{n+1}}	${\displaystyle{\displaystyle\Re z>0}}$	int(LegendreP(2*n, x)*(x)^((x + y*I)- 1), x = 0..1) = ((- 1)^(n)* pochhammer((1)/(2)-(1)/(2)*(x + y*I), n))/(2*pochhammer((1)/(2)*(x + y*I), n + 1))	Integrate[LegendreP[2*n, x]*(x)^((x + y*I)- 1), {x, 0, 1}, GenerateConditions->None] == Divide[(- 1)^(n)* Pochhammer[Divide[1,2]-Divide[1,2]*(x + y*I), n],2*Pochhammer[Divide[1,2]*(x + y*I), n + 1]]	Failure	Failure	Skipped - Because timed out	Failed [54 / 54] Result: Plus[Complex[-0.19540229885057472, 0.011494252873563225], NIntegrate[Complex[2.8897275468024644, -2.0119423961065603] Test Values: {1.5, 0, 1}]], {Rule[n, 1], Rule[x, 1.5], Rule[y, -1.5]} Result: Plus[Complex[0.03978779840848807, 0.061007957559681705], NIntegrate[Complex[14.158094475230552, -9.85742429396774] Test Values: {1.5, 0, 1}]], {Rule[n, 2], Rule[x, 1.5], Rule[y, -1.5]} ... skip entries to safe data
18.17.E39	${\displaystyle{\displaystyle\int_{0}^{1}P_{2n+1}\left(x\right)x^{z-1}\mathrm{d}x=\frac{(-1)^{n}{\left(1-\frac{1}{2}z\right)_{n}}}{2{\left(\frac{1}{2}+\frac{1}{2}z\right)_{n+1}}}}}$ \int_{0}^{1}\LegendrepolyP{2n+1}@{x}x^{z-1}\diff{x} = \frac{(-1)^{n}\Pochhammersym{1-\frac{1}{2}z}{n}}{2\Pochhammersym{\frac{1}{2}+\frac{1}{2}z}{n+1}}	${\displaystyle{\displaystyle\Re z>-1}}$	int(LegendreP(2*n + 1, x)*(x)^((x + y*I)- 1), x = 0..1) = ((- 1)^(n)* pochhammer(1 -(1)/(2)*(x + y*I), n))/(2*pochhammer((1)/(2)+(1)/(2)*(x + y*I), n + 1))	Integrate[LegendreP[2*n + 1, x]*(x)^((x + y*I)- 1), {x, 0, 1}, GenerateConditions->None] == Divide[(- 1)^(n)* Pochhammer[1 -Divide[1,2]*(x + y*I), n],2*Pochhammer[Divide[1,2]+Divide[1,2]*(x + y*I), n + 1]]	Failure	Failure	Failed [54 / 54] Result: .1141366199-.1434447856*I Test Values: {x = 3/2, y = -3/2, n = 1} Result: -.1797435469+.6231194668e-1*I Test Values: {x = 3/2, y = -3/2, n = 2} ... skip entries to safe data	Failed [54 / 54] Result: Plus[Complex[-0.058823529411764705, 0.0980392156862745], NIntegrate[Complex[6.21919624203139, -4.330049939446727] Test Values: {1.5, 0, 1}]], {Rule[n, 1], Rule[x, 1.5], Rule[y, -1.5]} Result: Plus[Complex[0.04824851288830139, -0.012998457810090328], NIntegrate[Complex[33.25149808949738, -23.151005642155518] Test Values: {1.5, 0, 1}]], {Rule[n, 2], Rule[x, 1.5], Rule[y, -1.5]} ... skip entries to safe data
18.17.E40	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-ax}L^{(\alpha)}_{n}\left(bx\right)x^{z-1}\mathrm{d}x=\frac{\Gamma\left(z+n\right)}{n!}\*{(a-b)^{n}}a^{-n-z}\*{{}_{2}F_{1}}\left({-n,1+\alpha-z\atop 1-n-z};\frac{a}{a-b}\right)}}$ \int_{0}^{\infty}e^{-ax}\LaguerrepolyL[\alpha]{n}@{bx}x^{z-1}\diff{x} = \frac{\EulerGamma@{z+n}}{n!}\*{(a-b)^{n}}a^{-n-z}\*\genhyperF{2}{1}@@{-n,1+\alpha-z}{1-n-z}{\frac{a}{a-b}}	${\displaystyle{\displaystyle\Re a>0,\Re z>0,\Re(z+n)>0}}$	int(exp(- a*x)*LaguerreL(n, alpha, b*x)*(x)^((x + y*I)- 1), x = 0..infinity) = (GAMMA((x + y*I)+ n))/(factorial(n))*(a - b)^(n)*(a)^(- n -(x + y*I))* hypergeom([- n , 1 + alpha -(x + y*I)], [1 - n -(x + y*I)], (a)/(a - b))	Integrate[Exp[- a*x]*LaguerreL[n, \[Alpha], b*x]*(x)^((x + y*I)- 1), {x, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[(x + y*I)+ n],(n)!]*(a - b)^(n)*(a)^(- n -(x + y*I))* HypergeometricPFQ[{- n , 1 + \[Alpha]-(x + y*I)}, {1 - n -(x + y*I)}, Divide[a,a - b]]	Missing Macro Error	Aborted	-	Skipped - Because timed out
18.17.E45	${\displaystyle{\displaystyle(n+\tfrac{1}{2})(1+x)^{\frac{1}{2}}\int_{-1}^{x}(x-t)^{-\frac{1}{2}}P_{n}\left(t\right)\mathrm{d}t=T_{n}\left(x\right)+T_{n+1}\left(x\right)}}$ (n+\tfrac{1}{2})(1+x)^{\frac{1}{2}}\int_{-1}^{x}(x-t)^{-\frac{1}{2}}\LegendrepolyP{n}@{t}\diff{t} = \ChebyshevpolyT{n}@{x}+\ChebyshevpolyT{n+1}@{x}		(n +(1)/(2))*(1 + x)^((1)/(2))* int((x - t)^(-(1)/(2))* LegendreP(n, t), t = - 1..x) = ChebyshevT(n, x)+ ChebyshevT(n + 1, x)	(n +Divide[1,2])*(1 + x)^(Divide[1,2])* Integrate[(x - t)^(-Divide[1,2])* LegendreP[n, t], {t, - 1, x}, GenerateConditions->None] == ChebyshevT[n, x]+ ChebyshevT[n + 1, x]	Failure	Failure	Successful [Tested: 9]	Successful [Tested: 9]
18.17.E46	${\displaystyle{\displaystyle(n+\tfrac{1}{2})(1-x)^{\frac{1}{2}}\int_{x}^{1}(t-x)^{-\frac{1}{2}}P_{n}\left(t\right)\mathrm{d}t=T_{n}\left(x\right)-T_{n+1}\left(x\right)}}$ (n+\tfrac{1}{2})(1-x)^{\frac{1}{2}}\int_{x}^{1}(t-x)^{-\frac{1}{2}}\LegendrepolyP{n}@{t}\diff{t} = \ChebyshevpolyT{n}@{x}-\ChebyshevpolyT{n+1}@{x}		(n +(1)/(2))*(1 - x)^((1)/(2))* int((t - x)^(-(1)/(2))* LegendreP(n, t), t = x..1) = ChebyshevT(n, x)- ChebyshevT(n + 1, x)	(n +Divide[1,2])*(1 - x)^(Divide[1,2])* Integrate[(t - x)^(-Divide[1,2])* LegendreP[n, t], {t, x, 1}, GenerateConditions->None] == ChebyshevT[n, x]- ChebyshevT[n + 1, x]	Failure	Failure	Successful [Tested: 9]	Successful [Tested: 9]
18.17.E47	${\displaystyle{\displaystyle\int_{0}^{x}t^{\alpha}\frac{L^{(\alpha)}_{m}\left(t\right)}{L^{(\alpha)}_{m}\left(0\right)}(x-t)^{\beta}\frac{L^{(\beta)}_{n}\left(x-t\right)}{L^{(\beta)}_{n}\left(0\right)}\mathrm{d}t=\frac{\Gamma\left(\alpha+1\right)\Gamma\left(\beta+1\right)}{\Gamma\left(\alpha+\beta+2\right)}x^{\alpha+\beta+1}\frac{L^{(\alpha+\beta+1)}_{m+n}\left(x\right)}{L^{(\alpha+\beta+1)}_{m+n}\left(0\right)}}}$ \int_{0}^{x}t^{\alpha}\frac{\LaguerrepolyL[\alpha]{m}@{t}}{\LaguerrepolyL[\alpha]{m}@{0}}(x-t)^{\beta}\frac{\LaguerrepolyL[\beta]{n}@{x-t}}{\LaguerrepolyL[\beta]{n}@{0}}\diff{t} = \frac{\EulerGamma@{\alpha+1}\EulerGamma@{\beta+1}}{\EulerGamma@{\alpha+\beta+2}}x^{\alpha+\beta+1}\frac{\LaguerrepolyL[\alpha+\beta+1]{m+n}@{x}}{\LaguerrepolyL[\alpha+\beta+1]{m+n}@{0}}	${\displaystyle{\displaystyle\Re(\alpha+1)>0,\Re(\beta+1)>0,\Re(\alpha+\beta+2)>0}}$	int((t)^(alpha)*(LaguerreL(m, alpha, t))/(LaguerreL(m, alpha, 0))*(x - t)^(beta)*(LaguerreL(n, beta, x - t))/(LaguerreL(n, beta, 0)), t = 0..x) = (GAMMA(alpha + 1)*GAMMA(beta + 1))/(GAMMA(alpha + beta + 2))*(x)^(alpha + beta + 1)*(LaguerreL(m + n, alpha + beta + 1, x))/(LaguerreL(m + n, alpha + beta + 1, 0))	Integrate[(t)^\[Alpha]*Divide[LaguerreL[m, \[Alpha], t],LaguerreL[m, \[Alpha], 0]]*(x - t)^\[Beta]*Divide[LaguerreL[n, \[Beta], x - t],LaguerreL[n, \[Beta], 0]], {t, 0, x}, GenerateConditions->None] == Divide[Gamma[\[Alpha]+ 1]*Gamma[\[Beta]+ 1],Gamma[\[Alpha]+ \[Beta]+ 2]]*(x)^(\[Alpha]+ \[Beta]+ 1)*Divide[LaguerreL[m + n, \[Alpha]+ \[Beta]+ 1, x],LaguerreL[m + n, \[Alpha]+ \[Beta]+ 1, 0]]	Missing Macro Error	Failure	-	Manual Skip!
18.17.E48	${\displaystyle{\displaystyle\int_{-\infty}^{\infty}H_{m}\left(y\right)e^{-y^{2}}H_{n}\left(x-y\right)e^{-(x-y)^{2}}\mathrm{d}y=\pi^{\frac{1}{2}}2^{-\frac{1}{2}(m+n+1)}H_{m+n}\left(2^{-\frac{1}{2}}x\right)e^{-\frac{1}{2}x^{2}}}}$ \int_{-\infty}^{\infty}\HermitepolyH{m}@{y}e^{-y^{2}}\HermitepolyH{n}@{x-y}e^{-(x-y)^{2}}\diff{y} = \pi^{\frac{1}{2}}2^{-\frac{1}{2}(m+n+1)}\HermitepolyH{m+n}@{2^{-\frac{1}{2}}x}e^{-\frac{1}{2}x^{2}}		int(HermiteH(m, y)*exp(- (y)^(2))*HermiteH(n, x - y)*exp(-(x - y)^(2)), y = - infinity..infinity) = (Pi)^((1)/(2))* (2)^(-(1)/(2)*(m + n + 1))* HermiteH(m + n, (2)^(-(1)/(2))* x)*exp(-(1)/(2)*(x)^(2))	Integrate[HermiteH[m, y]*Exp[- (y)^(2)]*HermiteH[n, x - y]*Exp[-(x - y)^(2)], {y, - Infinity, Infinity}, GenerateConditions->None] == (Pi)^(Divide[1,2])* (2)^(-Divide[1,2]*(m + n + 1))* HermiteH[m + n, (2)^(-Divide[1,2])* x]*Exp[-Divide[1,2]*(x)^(2)]	Failure	Aborted	Successful [Tested: 27]	Skipped - Because timed out
18.17.E49	${\displaystyle{\displaystyle\int_{-\infty}^{\infty}H_{\ell}\left(x\right)H_{m}\left(x\right)H_{n}\left(x\right)e^{-x^{2}}\mathrm{d}x=\frac{2^{\frac{1}{2}(\ell+m+n)}\ell\,!\,m\,!\,n\,!\,\sqrt{\pi}}{(\tfrac{1}{2}\ell+\tfrac{1}{2}m-\tfrac{1}{2}n)\,!\,(\tfrac{1}{2}m+\tfrac{1}{2}n-\tfrac{1}{2}\ell\,)\,!\,(\tfrac{1}{2}n+\tfrac{1}{2}\ell-\tfrac{1}{2}m\,)\,!}}}$ \int_{-\infty}^{\infty}\HermitepolyH{\ell}@{x}\HermitepolyH{m}@{x}\HermitepolyH{n}@{x}e^{-x^{2}}\diff{x} = \frac{2^{\frac{1}{2}(\ell+m+n)}\ell\,!\,m\,!\,n\,!\,\sqrt{\pi}}{(\tfrac{1}{2}\ell+\tfrac{1}{2}m-\tfrac{1}{2}n)\,!\,(\tfrac{1}{2}m+\tfrac{1}{2}n-\tfrac{1}{2}\ell\,)\,!\,(\tfrac{1}{2}n+\tfrac{1}{2}\ell-\tfrac{1}{2}m\,)\,!}		int(HermiteH(ell, x)*HermiteH(m, x)*HermiteH(n, x)*exp(- (x)^(2)), x = - infinity..infinity) = ((2)^((1)/(2)*(ell + m + n))* factorial(ell)*factorial(m)*factorial(n)*sqrt(Pi))/(factorial((1)/(2)*ell +(1)/(2)*m -(1)/(2)*n)*factorial((1)/(2)*m +(1)/(2)*n -(1)/(2)*ell)*factorial((1)/(2)*n +(1)/(2)*ell -(1)/(2)*m))	Integrate[HermiteH[\[ScriptL], x]*HermiteH[m, x]*HermiteH[n, x]*Exp[- (x)^(2)], {x, - Infinity, Infinity}, GenerateConditions->None] == Divide[(2)^(Divide[1,2]*(\[ScriptL]+ m + n))* (\[ScriptL])!*(m)!*(n)!*Sqrt[Pi],(Divide[1,2]*\[ScriptL]+Divide[1,2]*m -Divide[1,2]*n)!*(Divide[1,2]*m +Divide[1,2]*n -Divide[1,2]*\[ScriptL])!*(Divide[1,2]*n +Divide[1,2]*\[ScriptL]-Divide[1,2]*m)!]	Failure	Aborted	Error	Skipped - Because timed out
18.18.E8	${\displaystyle{\displaystyle C^{(\lambda)}_{n}\left(\cos\theta_{1}\cos\theta_{2}+\sin\theta_{1}\sin\theta_{2}\cos\phi\right)=\sum_{\ell=0}^{n}2^{2\ell}(n-\ell)!\frac{2\lambda+2\ell-1}{2\lambda-1}\frac{({\left(\lambda\right)_{\ell}})^{2}}{{\left(2\lambda\right)_{n+\ell}}}(\sin\theta_{1})^{\ell}C^{(\lambda+\ell)}_{n-\ell}\left(\cos\theta_{1}\right)(\sin\theta_{2})^{\ell}C^{(\lambda+\ell)}_{n-\ell}\left(\cos\theta_{2}\right)C^{(\lambda-\frac{1}{2})}_{\ell}\left(\cos\phi\right)}}$ \ultrasphpoly{\lambda}{n}@{\cos@@{\theta_{1}}\cos@@{\theta_{2}}+\sin@@{\theta_{1}}\sin@@{\theta_{2}}\cos@@{\phi}} = \sum_{\ell=0}^{n}2^{2\ell}(n-\ell)!\frac{2\lambda+2\ell-1}{2\lambda-1}\frac{(\Pochhammersym{\lambda}{\ell})^{2}}{\Pochhammersym{2\lambda}{n+\ell}}(\sin@@{\theta_{1}})^{\ell}\ultrasphpoly{\lambda+\ell}{n-\ell}@{\cos@@{\theta_{1}}}(\sin@@{\theta_{2}})^{\ell}\ultrasphpoly{\lambda+\ell}{n-\ell}@{\cos@@{\theta_{2}}}\ultrasphpoly{\lambda-\frac{1}{2}}{\ell}@{\cos@@{\phi}}	${\displaystyle{\displaystyle\lambda>0,\lambda\neq\frac{1}{2}}}$	GegenbauerC(n, lambda, cos(theta[1])*cos(theta[2])+ sin(theta[1])*sin(theta[2])*cos(phi)) = sum((2)^(2*ell)*factorial(n - ell)*(2*lambda + 2*ell - 1)/(2*lambda - 1)*((pochhammer(lambda, ell))^(2))/(pochhammer(2*lambda, n + ell))*(sin(theta[1]))^(ell)* GegenbauerC(n - ell, lambda + ell, cos(theta[1]))*(sin(theta[2]))^(ell)* GegenbauerC(n - ell, lambda + ell, cos(theta[2]))*GegenbauerC(ell, lambda -(1)/(2), cos(phi)), ell = 0..n)	GegenbauerC[n, \[Lambda], Cos[Subscript[\[Theta], 1]]*Cos[Subscript[\[Theta], 2]]+ Sin[Subscript[\[Theta], 1]]*Sin[Subscript[\[Theta], 2]]*Cos[\[Phi]]] == Sum[(2)^(2*\[ScriptL])*(n - \[ScriptL])!*Divide[2*\[Lambda]+ 2*\[ScriptL]- 1,2*\[Lambda]- 1]*Divide[(Pochhammer[\[Lambda], \[ScriptL]])^(2),Pochhammer[2*\[Lambda], n + \[ScriptL]]]*(Sin[Subscript[\[Theta], 1]])^\[ScriptL]* GegenbauerC[n - \[ScriptL], \[Lambda]+ \[ScriptL], Cos[Subscript[\[Theta], 1]]]*(Sin[Subscript[\[Theta], 2]])^\[ScriptL]* GegenbauerC[n - \[ScriptL], \[Lambda]+ \[ScriptL], Cos[Subscript[\[Theta], 2]]]*GegenbauerC[\[ScriptL], \[Lambda]-Divide[1,2], Cos[\[Phi]]], {\[ScriptL], 0, n}, GenerateConditions->None]	Failure	Aborted	Successful [Tested: 300]	Skipped - Because timed out
18.18.E9	${\displaystyle{\displaystyle P_{n}\left(\cos\theta_{1}\cos\theta_{2}+\sin\theta_{1}\sin\theta_{2}\cos\phi\right)={P_{n}\left(\cos\theta_{1}\right)P_{n}\left(\cos\theta_{2}\right)+2\sum_{\ell=1}^{n}\frac{(n-\ell)!\;(n+\ell)!}{2^{2\ell}(n!)^{2}}(\sin\theta_{1})^{\ell}P^{(\ell,\ell)}_{n-\ell}\left(\cos\theta_{1}\right)(\sin\theta_{2})^{\ell}P^{(\ell,\ell)}_{n-\ell}\left(\cos\theta_{2}\right)\cos\left(\ell\phi\right)}}}$ \LegendrepolyP{n}@{\cos@@{\theta_{1}}\cos@@{\theta_{2}}+\sin@@{\theta_{1}}\sin@@{\theta_{2}}\cos@@{\phi}} = {\LegendrepolyP{n}@{\cos@@{\theta_{1}}}\LegendrepolyP{n}@{\cos@@{\theta_{2}}}+2\sum_{\ell=1}^{n}\frac{(n-\ell)!\;(n+\ell)!}{2^{2\ell}(n!)^{2}}(\sin@@{\theta_{1}})^{\ell}\JacobipolyP{\ell}{\ell}{n-\ell}@{\cos@@{\theta_{1}}}(\sin@@{\theta_{2}})^{\ell}\JacobipolyP{\ell}{\ell}{n-\ell}@{\cos@@{\theta_{2}}}\cos@{\ell\phi}}		LegendreP(n, cos(theta[1])*cos(theta[2])+ sin(theta[1])*sin(theta[2])*cos(phi)) = LegendreP(n, cos(theta[1]))*LegendreP(n, cos(theta[2]))+ 2*sum((factorial(n - ell)*factorial(n + ell))/((2)^(2*ell)*(factorial(n))^(2))*(sin(theta[1]))^(ell)* JacobiP(n - ell, ell, ell, cos(theta[1]))*(sin(theta[2]))^(ell)* JacobiP(n - ell, ell, ell, cos(theta[2]))*cos(ell*phi), ell = 1..n)	LegendreP[n, Cos[Subscript[\[Theta], 1]]*Cos[Subscript[\[Theta], 2]]+ Sin[Subscript[\[Theta], 1]]*Sin[Subscript[\[Theta], 2]]*Cos[\[Phi]]] == LegendreP[n, Cos[Subscript[\[Theta], 1]]]*LegendreP[n, Cos[Subscript[\[Theta], 2]]]+ 2*Sum[Divide[(n - \[ScriptL])!*(n + \[ScriptL])!,(2)^(2*\[ScriptL])*((n)!)^(2)]*(Sin[Subscript[\[Theta], 1]])^\[ScriptL]* JacobiP[n - \[ScriptL], \[ScriptL], \[ScriptL], Cos[Subscript[\[Theta], 1]]]*(Sin[Subscript[\[Theta], 2]])^\[ScriptL]* JacobiP[n - \[ScriptL], \[ScriptL], \[ScriptL], Cos[Subscript[\[Theta], 2]]]*Cos[\[ScriptL]*\[Phi]], {\[ScriptL], 1, n}, GenerateConditions->None]	Failure	Aborted	Successful [Tested: 300]	Skipped - Because timed out
18.18.E12	${\displaystyle{\displaystyle\frac{L^{(\alpha)}_{n}\left(\lambda x\right)}{L^{(\alpha)}_{n}\left(0\right)}=\sum_{\ell=0}^{n}\genfrac{(}{)}{0.0pt}{}{n}{\ell}\lambda^{\ell}(1-\lambda)^{n-\ell}\frac{L^{(\alpha)}_{\ell}\left(x\right)}{L^{(\alpha)}_{\ell}\left(0\right)}}}$ \frac{\LaguerrepolyL[\alpha]{n}@{\lambda x}}{\LaguerrepolyL[\alpha]{n}@{0}} = \sum_{\ell=0}^{n}\binom{n}{\ell}\lambda^{\ell}(1-\lambda)^{n-\ell}\frac{\LaguerrepolyL[\alpha]{\ell}@{x}}{\LaguerrepolyL[\alpha]{\ell}@{0}}		(LaguerreL(n, alpha, lambda*x))/(LaguerreL(n, alpha, 0)) = sum(binomial(n,ell)*(lambda)^(ell)*(1 - lambda)^(n - ell)*(LaguerreL(ell, alpha, x))/(LaguerreL(ell, alpha, 0)), ell = 0..n)	Divide[LaguerreL[n, \[Alpha], \[Lambda]*x],LaguerreL[n, \[Alpha], 0]] == Sum[Binomial[n,\[ScriptL]]*\[Lambda]^\[ScriptL]*(1 - \[Lambda])^(n - \[ScriptL])*Divide[LaguerreL[\[ScriptL], \[Alpha], x],LaguerreL[\[ScriptL], \[Alpha], 0]], {\[ScriptL], 0, n}, GenerateConditions->None]	Missing Macro Error	Failure	-	Skipped - Because timed out
18.18.E13	${\displaystyle{\displaystyle H_{n}\left(\lambda x\right)=\lambda^{n}\sum_{\ell=0}^{\left\lfloor n/2\right\rfloor}\frac{{\left(-n\right)_{2\ell}}}{\ell!}(1-\lambda^{-2})^{\ell}H_{n-2\ell}\left(x\right)}}$ \HermitepolyH{n}@{\lambda x} = \lambda^{n}\sum_{\ell=0}^{\floor{n/2}}\frac{\Pochhammersym{-n}{2\ell}}{\ell!}(1-\lambda^{-2})^{\ell}\HermitepolyH{n-2\ell}@{x}		HermiteH(n, lambda*x) = (lambda)^(n)* sum((pochhammer(- n, 2*ell))/(factorial(ell))*(1 - (lambda)^(- 2))^(ell)* HermiteH(n - 2*ell, x), ell = 0..floor(n/2))	HermiteH[n, \[Lambda]*x] == \[Lambda]^(n)* Sum[Divide[Pochhammer[- n, 2*\[ScriptL]],(\[ScriptL])!]*(1 - \[Lambda]^(- 2))^\[ScriptL]* HermiteH[n - 2*\[ScriptL], x], {\[ScriptL], 0, Floor[n/2]}, GenerateConditions->None]	Failure	Failure	Successful [Tested: 90]	Failed [90 / 90] Result: Complex[2.598076211353316, 1.4999999999999998] Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[2.5, 7.794228634059947] Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.18.E14	${\displaystyle{\displaystyle P^{(\gamma,\beta)}_{n}\left(x\right)=\dfrac{{\left(\beta+1\right)_{n}}}{{\left(\alpha+\beta+2\right)_{n}}}\sum_{\ell=0}^{n}\dfrac{\alpha+\beta+2\ell+1}{\alpha+\beta+1}\dfrac{{\left(\alpha+\beta+1\right)_{\ell}}{\left(n+\beta+\gamma+1\right)_{\ell}}}{{\left(\beta+1\right)_{\ell}}{\left(n+\alpha+\beta+2\right)_{\ell}}}\dfrac{{\left(\gamma-\alpha\right)_{n-\ell}}}{(n-\ell)!}P^{(\alpha,\beta)}_{\ell}\left(x\right)}}$ \JacobipolyP{\gamma}{\beta}{n}@{x} = \dfrac{\Pochhammersym{\beta+1}{n}}{\Pochhammersym{\alpha+\beta+2}{n}}\sum_{\ell=0}^{n}\dfrac{\alpha+\beta+2\ell+1}{\alpha+\beta+1}\dfrac{\Pochhammersym{\alpha+\beta+1}{\ell}\Pochhammersym{n+\beta+\gamma+1}{\ell}}{\Pochhammersym{\beta+1}{\ell}\Pochhammersym{n+\alpha+\beta+2}{\ell}}\dfrac{\Pochhammersym{\gamma-\alpha}{n-\ell}}{(n-\ell)!}\JacobipolyP{\alpha}{\beta}{\ell}@{x}		JacobiP(n, gamma, beta, x) = (pochhammer(beta + 1, n))/(pochhammer(alpha + beta + 2, n))*sum((alpha + beta + 2*ell + 1)/(alpha + beta + 1)*(pochhammer(alpha + beta + 1, ell)*pochhammer(n + beta + gamma + 1, ell))/(pochhammer(beta + 1, ell)*pochhammer(n + alpha + beta + 2, ell))*(pochhammer(gamma - alpha, n - ell))/(factorial(n - ell))*JacobiP(ell, alpha, beta, x), ell = 0..n)	JacobiP[n, \[Gamma], \[Beta], x] == Divide[Pochhammer[\[Beta]+ 1, n],Pochhammer[\[Alpha]+ \[Beta]+ 2, n]]*Sum[Divide[\[Alpha]+ \[Beta]+ 2*\[ScriptL]+ 1,\[Alpha]+ \[Beta]+ 1]*Divide[Pochhammer[\[Alpha]+ \[Beta]+ 1, \[ScriptL]]*Pochhammer[n + \[Beta]+ \[Gamma]+ 1, \[ScriptL]],Pochhammer[\[Beta]+ 1, \[ScriptL]]*Pochhammer[n + \[Alpha]+ \[Beta]+ 2, \[ScriptL]]]*Divide[Pochhammer[\[Gamma]- \[Alpha], n - \[ScriptL]],(n - \[ScriptL])!]*JacobiP[\[ScriptL], \[Alpha], \[Beta], x], {\[ScriptL], 0, n}, GenerateConditions->None]	Failure	Aborted	Failed [299 / 300] Result: -.361012173-.6250000000*I Test Values: {alpha = 3/2, beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, x = 3/2, n = 1} Result: -1.123113229-2.395332347*I Test Values: {alpha = 3/2, beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, x = 3/2, n = 2} ... skip entries to safe data	Skipped - Because timed out
18.18.E15	${\displaystyle{\displaystyle\left(\frac{1+x}{2}\right)^{n}=\frac{{\left(\beta+1\right)_{n}}}{{\left(\alpha+\beta+2\right)_{n}}}\sum_{\ell=0}^{n}\frac{\alpha+\beta+2\ell+1}{\alpha+\beta+1}\frac{{\left(\alpha+\beta+1\right)_{\ell}}{\left(n-\ell+1\right)_{\ell}}}{{\left(\beta+1\right)_{\ell}}{\left(n+\alpha+\beta+2\right)_{\ell}}}P^{(\alpha,\beta)}_{\ell}\left(x\right)}}$ \left(\frac{1+x}{2}\right)^{n} = \frac{\Pochhammersym{\beta+1}{n}}{\Pochhammersym{\alpha+\beta+2}{n}}\sum_{\ell=0}^{n}\frac{\alpha+\beta+2\ell+1}{\alpha+\beta+1}\frac{\Pochhammersym{\alpha+\beta+1}{\ell}\Pochhammersym{n-\ell+1}{\ell}}{\Pochhammersym{\beta+1}{\ell}\Pochhammersym{n+\alpha+\beta+2}{\ell}}\JacobipolyP{\alpha}{\beta}{\ell}@{x}		((1 + x)/(2))^(n) = (pochhammer(beta + 1, n))/(pochhammer(alpha + beta + 2, n))*sum((alpha + beta + 2*ell + 1)/(alpha + beta + 1)*(pochhammer(alpha + beta + 1, ell)*pochhammer(n - ell + 1, ell))/(pochhammer(beta + 1, ell)*pochhammer(n + alpha + beta + 2, ell))*JacobiP(ell, alpha, beta, x), ell = 0..n)	(Divide[1 + x,2])^(n) == Divide[Pochhammer[\[Beta]+ 1, n],Pochhammer[\[Alpha]+ \[Beta]+ 2, n]]*Sum[Divide[\[Alpha]+ \[Beta]+ 2*\[ScriptL]+ 1,\[Alpha]+ \[Beta]+ 1]*Divide[Pochhammer[\[Alpha]+ \[Beta]+ 1, \[ScriptL]]*Pochhammer[n - \[ScriptL]+ 1, \[ScriptL]],Pochhammer[\[Beta]+ 1, \[ScriptL]]*Pochhammer[n + \[Alpha]+ \[Beta]+ 2, \[ScriptL]]]*JacobiP[\[ScriptL], \[Alpha], \[Beta], x], {\[ScriptL], 0, n}, GenerateConditions->None]	Failure	Aborted	Successful [Tested: 81]	Failed [78 / 81] Result: Plus[1.25, Times[-0.125, Plus[Times[2.0, DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[-2, Plus[1, ], Plus[-1, Times[-1, ], 1], Plus[Times[-1, ], 1], Plus[1, , 1.5], Plus[1, , 1.5, 1.5], Plus[4, Times[2, ], 1.5, 1.5], []], Times[Plus[-1, Times[-1, ], 1], Plus[Times[-8, ], Times[-28, Power[, 2]], Times[-36, Power[, 3]], Times[-20, Power[, 4]], Times[-4, Power[, 5]], Times[8, 1], Times[28, , 1], Times[36, Power[, 2], 1], Times[20, Power[, 3], 1], Times[4, Power[, 4], 1], Times[48, , 1.5], Times[128, Power[, 2], 1.5], Times[124, Power[, 3], 1.5], Times[52, Power[, 4], 1.5], Times[8, Power[, 5], 1.5], Times[24, , 1, 1.5], Times[52, Power[, 2], 1, 1.5], Times[36, Power[, 3], 1, 1.5], Times[8, Power[, 4], 1, 1.5], Times[-18, , 1.5], Times[-46, Power[, 2], 1.5], Times[-38, Power[, 3], 1.5], Times[-10, Power[, 4], 1.5], Times[18, 1, 1.5], Times[46, , 1, 1.5], Times[38, Power[, 2], 1, 1.5], Times[10, Powe<syntaxhighlight lang=mathematica>Result: Plus[1.5625, Times[-0.07291666666666667, Plus[Times[2.0, DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[-2, Plus[1, ], Plus[-1, Times[-1, ], 2], Plus[Times[-1, ], 2], Plus[1, , 1.5], Plus[1, , 1.5, 1.5], Plus[4, Times[2, ], 1.5, 1.5], []], Times[Plus[-1, Times[-1, ], 2], Plus[Times[-8, ], Times[-28, Power[, 2]], Times[-36, Power[, 3]], Times[-20, Power[, 4]], Times[-4, Power[, 5]], Times[8, 2], Times[28, , 2], Times[36, Power[, 2], 2], Times[20, Power[, 3], 2], Times[4, Power[, 4], 2], Times[48, , 1.5], Times[128, Power[, 2], 1.5], Times[124, Power[, 3], 1.5], Times[52, Power[, 4], 1.5], Times[8, Power[, 5], 1.5], Times[24, , 2, 1.5], Times[52, Power[, 2], 2, 1.5], Times[36, Power[, 3], 2, 1.5], Times[8, Power[, 4], 2, 1.5], Times[-18, , 1.5], Times[-46, Power[, 2], 1.5], Times[-38, Power[, 3], 1.5], Times[-10, Power[, 4], 1.5], Times[18, 2, 1.5], Times[46, , 2, 1.5], Times[38, Power[, 2], 2, 1.5], Times[10, Power[, 3], 2, 1.5], Times[76, , 1.5, 1.5], Times[150, Power[, 2], 1.5, 1.5], Times[96, Power[, 3], 1.5, 1.5], Times[20, Power[, 4], 1.5, 1.5], Times[26, , 2, 1.5, 1.5], Times[36, Power[, 2], 2, 1.5, 1.5], Times[12, Power[, 3], 2, 1.5, 1.5], Times[-6, , Power[1.5, 2]], Times[-13, Power[, 2], Power[1.5, 2]], Times[-6, Power[, 3], Power[1.5, 2]], Times[12, 2, Power[1.5, 2]], Times[23, , 2, Power[1.5, 2]], Times[10, Power[, 2], 2, Power[1.5, 2]], Times[44, , 1.5, Power[1.5, 2]], Times[57, Power[, 2], 1.5, Power[1.5, 2]], Times[18, Power[, 3], 1.5, Power[1.5, 2]], Times[9, , 2, 1.5, Power[1.5, 2]], Times[6, Power[, 2], 2, 1.5, Power[1.5, 2]], Times[3, , Power[1.5, 3]], Times[Power[, 2], Power[1.5, 3]], Times[2, 2, Power[1.5, 3]], Times[3, , 2, Power[1.5, 3]], Times[11, , 1.5, Power[1.5, 3]], Times[7, Power[, 2], 1.5, Power[1.5, 3]], Times[, 2, 1.5, Power[1.5, 3]], Times[, Power[1.5, 4]], Times[, 1.5, Power[1.5, 4]], Times[-10, , 1.5], Times[-26, Power[, 2], 1.5], Times[-22, Power[, 3], 1.5], Times[-6, Power[, 4], 1.5], Times[10, 2, 1.5], Times[26, , 2, 1.5], Times[22, Power[, 2], 2, 1.5], Times[6, Power[, 3], 2, 1.5], Times[76, , 1.5, 1.5], Times[150, Power[, 2], 1.5, 1.5], Times[96, Power[, 3], 1.5, 1.5], Times[20, Power[, 4], 1.5, 1.5], Times[26, , 2, 1.5, 1.5], Times[36, Power[, 2], 2, 1.5, 1.5], Times[12, Power[, 3], 2, 1.5, 1.5], Times[-14, , 1.5, 1.5], Times[-24, Power[, 2], 1.5, 1.5], Times[-10, Power[, 3], 1.5, 1.5], Times[14, 2, 1.5, 1.5], Times[24, , 2, 1.5, 1.5], Times[10, Power[, 2], 2, 1.5, 1.5], Times[88, , 1.5, 1.5, 1.5], Times[114, Power[, 2], 1.5, 1.5, 1.5], Times[36, Power[, 3], 1.5, 1.5, 1.5], Times[18, , 2, 1.5, 1.5, 1.5], Times[12, Power[, 2], 2, 1.5, 1.5, 1.5], Times[, Power[1.5, 2], 1.5], Times[-1, Power[, 2], Power[1.5, 2], 1.5], Times[4, 2, Power[1.5, 2], 1.5], Times[5, , 2, Power[1.5, 2], 1.5], Times[33, , 1.5, Power[1.5, 2], 1.5], Times[21, Power[, 2], 1.5, Power[1.5, 2], 1.5], Times[3, , 2, 1.5, Power[1.5, 2], 1.5], Times[2, , Power[1.5, 3], 1.5], Times[4, , 1.5, Power[1.5, 3], 1.5], Times[-8, , Power[1.5, 2]], Times[-11, Power[, 2], Power[1.5, 2]], Times[-4, Power[, 3], Power[1.5, 2]], Times[2, 2, Power[1.5, 2]], Times[, 2, Power[1.5, 2]], Times[44, , 1.5, Power[1.5, 2]], Times[57, Power[, 2], 1.5, Power[1.5, 2]], Times[18, Power[, 3], 1.5, Power[1.5, 2]], Times[9, , 2, 1.5, Power[1.5, 2]], Times[6, Power[, 2], 2, 1.5, Power[1.5, 2]], Times[-7, , 1.5, Power[1.5, 2]], Times[-5, Power[, 2], 1.5, Power[1.5, 2]], Times[2, 2, 1.5, Power[1.5, 2]], Times[, 2, 1.5, Power[1.5, 2]], Times[33, , 1.5, 1.5, Power[1.5, 2]], Times[21, Power[, 2], 1.5, 1.5, Power[1.5, 2]], Times[3, , 2, 1.5, 1.5, Power[1.5, 2]], Times[6, , 1.5, Power[1.5, 2], Power[1.5, 2]], Times[-5, , Power[1.5, 3]], Times[-3, Power[, 2], Power[1.5, 3]], Times[-1, , 2, Power[1.5, 3]], Times[11, , 1.5, Power[1.5, 3]], Times[7, Power[, 2], 1.5, Power[1.5, 3]], Times[, 2, 1.5, Power[1.5, 3]], Times[-2, , 1.5, Power[1.5, 3]], Times[4, , 1.5, 1.5, Power[1.5, 3]], Times[-1, , Power[1.5, 4]], Times[, 1.5, Power[1.5, 4]]], [Plus[1, ]]], Times[, Plus[2, , 2, 1.5, 1.5], Plus[-24, Times[-68, ], Times[-68, Power[, 2]], Times[-28, Power[, 3]], Times[-4, Power[, 4]], Times[-8, 2], Times[-20, , 2], Times[-16, Power[, 2], 2], Times[-4, Power[, 3], 2], Times[24, 1.5], Times[76, , 1.5], Times[88, Power[, 2], 1.5], Times[44, Power[, 3], 1.5], Times[8, Power[, 4], 1.5], Times[-24, 2, 1.5], Times[-52, , 2, 1.5], Times[-36, Power[, 2], 2, 1.5], Times[-8, Power[, 3], 2, 1.5], Times[-20, 1.5], Times[-42, , 1.5], Times[-28, Power[, 2], 1.5], Times[-6, Power[, 3], 1.5], Times[-4, 2, 1.5], Times[-6, , 2, 1.5], Times[-2, Power[, 2], 2, 1.5], Times[26, 1.5, 1.5], Times[62, , 1.5, 1.5], Times[48, Power[, 2], 1.5, 1.5], Times[12, Power[, 3], 1.5, 1.5], Times[-26, 2, 1.5, 1.5], Times[-36, , 2, 1.5, 1.5], Times[-12, Power[, 2], 2, 1.5, 1.5], Times[-1, Power[1.5, 2]], Times[-1, , Power[1.5, 2]], Times[-3, 2, Power[1.5, 2]], Times[-2, , 2, Power[1.5, 2]], Times[9, 1.5, Power[1.5, 2]], Times[15, , 1.5, Power[1.5, 2]], Times[6, Power[, 2], 1.5, Power[1.5, 2]], Times[-9, 2, 1.5, Power[1.5, 2]], Times[-6, , 2, 1.5, Power[1.5, 2]], Power[1.5, 3], Times[, Power[1.5, 3]], Times[-1, 2, Power[1.5, 3]], Times[1.5, Power[1.5, 3]], Times[, 1.5, Power[1.5, 3]], Times[-1, 2, 1.5, Power[1.5, 3]], Times[-32, 1.5], Times[-70, , 1.5], Times[-48, Power[, 2], 1.5], Times[-10, Power[, 3], 1.5], Times[-8, 2, 1.5], Times[-14, , 2, 1.5], Times[-6, Power[, 2], 2, 1.5], Times[26, 1.5, 1.5], Times[62, , 1.5, 1.5], Times[48, Power[, 2], 1.5, 1.5], Times[12, Power[, 3], 1.5, 1.5], Times[-26, 2, 1.5, 1.5], Times[-36, , 2, 1.5, 1.5], Times[-12, Power[, 2], 2, 1.5, 1.5], Times[-18, 1.5, 1.5], Times[-28, , 1.5, 1.5], Times[-10, Power[, 2], 1.5, 1.5], Times[-2, 2, 1.5, 1.5], Times[-2, , 2, 1.5, 1.5], Times[18, 1.5, 1.5, 1.5], Times[30, , 1.5, 1.5, 1.5], Times[12, Power[, 2], 1.5, 1.5, 1.5], Times[-18, 2, 1.5, 1.5, 1.5], Times[-12, , 2, 1.5, 1.5, 1.5], Times[-1, Power[1.5, 2], 1.5], Times[-1, , Power[1.5, 2], 1.5], Times[-1, 2, Power[1.5, 2], 1.5], Times[3, 1.5, Power[1.5, 2], 1.5], Times[3, , 1.5, Power[1.5, 2], 1.5], Times[-3, 2, 1.5, Power[1.5, 2], 1.5], Times[-17, Power[1.5, 2]], Times[-27, , Power[1.5, 2]], Times[-10, Power[, 2], Power[1.5, 2]], Times[2, Power[1.5, 2]], Times[9, 1.5, Power[1.5, 2]], Times[15, , 1.5, Power[1.5, 2]], Times[6, Power[, 2], 1.5, Power[1.5, 2]], Times[-9, 2, 1.5, Power[1.5, 2]], Times[-6, , 2, 1.5, Power[1.5, 2]], Times[-5, 1.5, Power[1.5, 2]], Times[-5, , 1.5, Power[1.5, 2]], Times[2, 1.5, Power[1.5, 2]], Times[3, 1.5, 1.5, Power[1.5, 2]], Times[3, , 1.5, 1.5, Power[1.5, 2]], Times[-3, 2, 1.5, 1.5, Power[1.5, 2]], Times[-3, Power[1.5, 3]], Times[-3, , Power[1.5, 3]], Times[2, Power[1.5, 3]], Times[1.5, Power[1.5, 3]], Times[, 1.5, Power[1.5, 3]], Times[-1, 2, 1.5, Power[1.5, 3]]], [Plus[2, ]]], Times[2, , Plus[1, ], Plus[2, , 1.5], Plus[2, Times[2, ], 1.5, 1.5], Plus[2, , 2, 1.5, 1.5], Plus[3, , 2, 1.5, 1.5], [Plus[3, ]]]], 0], Equal[[1], 0], Equal[[2], Times[Rational[1, 2], 2, Power[Plus[1, 1.5], -1], Plus[1, 1.5, 1.5], Power[Plus[2, 2, 1.5, 1.5], -1], Plus[1.5, Times[-1, 1.5], Times[1.5, Plus[2, 1.5, 1.5]]]]], Equal[[3], Plus[Times[Rational[1, 2], 2, Power[Plus[1, 1.5], -1], Plus[1, 1.5, 1.5], Power[Plus[2, 2, 1.5, 1.5], -1], Plus[1.5, Times[-1, 1.5], Times[1.5, Plus[2, 1.5, 1.5]]]], Times[Rational[1, 2], Plus[-1, 2], 2, Power[Plus[1, 1.5], -1], Power[Plus[2, 1.5], -1], Plus[1, 1.5, 1.5], Power[Plus[2, 1.5, 1.5], -1], Power[Plus[2, 2, 1.5, 1.5], -1], Power[Plus[3, 2, 1.5, 1.5], -1], Plus[Times[-2, Plus[1, 1.5], Plus[1, 1.5], Plus[4, 1.5, 1.5]], Times[Rational[1, 2], Plus[3, 1.5, 1.5], Plus[Times[8, 1.5], Times[6, 1.5, 1.5], Power[1.5, 2], Times[1.5, Power[1.5, 2]], Times[6, 1.5, 1.5], Times[2, 1.5, 1.5, 1.5], Times[-1, Power[1.5, 2]], Times[1.5, Power[1.5, 2]]], Plus[1.5, Times[-1, 1.5], Times[1.5, Plus[2, 1.5, 1.5]]]]]]]]}]][3.0]], Times[4.0, DifferenceRoot[Function[{, }, {Equal[Plus[Times[-2, Plus[-1, Times[-1, ], 2], Plus[Times[-1, ], 2], Plus[1, , 1.5], Plus[1, , 1.5, 1.5], Plus[4, Times[2, ], 1.5, 1.5], []], Times[Plus[-1, Times[-1, ], 2], Plus[Times[-8, ], Times[-20, Power[, 2]], Times[-16, Power[, 3]], Times[-4, Power[, 4]], Times[8, 2], Times[20, , 2], Times[16, Power[, 2], 2], Times[4, Power[, 3], 2], Times[48, 1.5], Times[128, , 1.5], Times[124, Power[, 2], 1.5], Times[52, Power[, 3], 1.5], Times[8, Power[, 4], 1.5], Times[24, 2, 1.5], Times[52, , 2, 1.5], Times[36, Power[, 2], 2, 1.5], Times[8, Power[, 3], 2, 1.5], Times[-18, , 1.5], Times[-28, Power[, 2], 1.5], Times[-10, Power[, 3], 1.5], Times[18, 2, 1.5], Times[28, , 2, 1.5], Times[10, Power[, 2], 2, 1.5], Times[76, 1.5, 1.5], Times[150, , 1.5, 1.5], Times[96, Power[, 2], 1.5, 1.5], Times[20, Power[, 3], 1.5, 1.5], Times[26, 2, 1.5, 1.5], Times[36, , 2, 1.5, 1.5], Times[12, Power[, 2], 2, 1.5, 1.5], Times[6, Power[1.5, 2]], Times[-5, , Power[1.5, 2]], Times[-6, Power[, 2], Power[1.5, 2]], Times[15, 2, Power[1.5, 2]], Times[10, , 2, Power[1.5, 2]], Times[44, 1.5, Power[1.5, 2]], Times[57, , 1.5, Power[1.5, 2]], Times[18, Power[, 2], 1.5, Power[1.5, 2]], Times[9, 2, 1.5, Power[1.5, 2]], Times[6, , 2, 1.5, Power[1.5, 2]], Times[5, Power[1.5, 3]], Times[, Power[1.5, 3]], Times[3, 2, Power[1.5, 3]], Times[11, 1.5, Power[1.5, 3]], Times[7, , 1.5, Power[1.5, 3]], Times[2, 1.5, Power[1.5, 3]], Power[1.5, 4], Times[1.5, Power[1.5, 4]], Times[-10, , 1.5], Times[-16, Power[, 2], 1.5], Times[-6, Power[, 3], 1.5], Times[10, 2, 1.5], Times[16, , 2, 1.5], Times[6, Power[, 2], 2, 1.5], Times[76, 1.5, 1.5], Times[150, , 1.5, 1.5], Times[96, Power[, 2], 1.5, 1.5], Times[20, Power[, 3], 1.5, 1.5], Times[26, 2, 1.5, 1.5], Times[36, , 2, 1.5, 1.5], Times[12, Power[, 2], 2, 1.5, 1.5], Times[-14, , 1.5, 1.5], Times[-10, Power[, 2], 1.5, 1.5], Times[14, 2, 1.5, 1.5], Times[10, , 2, 1.5, 1.5], Times[88, 1.5, 1.5, 1.5], Times[114, , 1.5, 1.5, 1.5], Times[36, Power[, 2], 1.5, 1.5, 1.5], Times[18, 2, 1.5, 1.5, 1.5], Times[12, , 2, 1.5, 1.5, 1.5], Times[5, Power[1.5, 2], 1.5], Times[-1, , Power[1.5, 2], 1.5], Times[5, 2, Power[1.5, 2], 1.5], Times[33, 1.5, Power[1.5, 2], 1.5], Times[21, , 1.5, Power[1.5, 2], 1.5], Times[3, 2, 1.5, Power[1.5, 2], 1.5], Times[2, Power[1.5, 3], 1.5], Times[4, 1.5, Power[1.5, 3], 1.5], Times[-6, Power[1.5, 2]], Times[-9, , Power[1.5, 2]], Times[-4, Power[, 2], Power[1.5, 2]], Times[-1, 2, Power[1.5, 2]], Times[44, 1.5, Power[1.5, 2]], Times[57, , 1.5, Power[1.5, 2]], Times[18, Power[, 2], 1.5, Power[1.5, 2]], Times[9, 2, 1.5, Power[1.5, 2]], Times[6, , 2, 1.5, Power[1.5, 2]], Times[-5, 1.5, Power[1.5, 2]], Times[-5, , 1.5, Power[1.5, 2]], Times[2, 1.5, Power[1.5, 2]], Times[33, 1.5, 1.5, Power[1.5, 2]], Times[21, , 1.5, 1.5, Power[1.5, 2]], Times[3, 2, 1.5, 1.5, Power[1.5, 2]], Times[6, 1.5, Power[1.5, 2], Power[1.5, 2]], Times[-5, Power[1.5, 3]], Times[-3, , Power[1.5, 3]], Times[-1, 2, Power[1.5, 3]], Times[11, 1.5, Power[1.5, 3]], Times[7, , 1.5, Power[1.5, 3]], Times[2, 1.5, Power[1.5, 3]], Times[-2, 1.5, Power[1.5, 3]], Times[4, 1.5, 1.5, Power[1.5, 3]], Times[-1, Power[1.5, 4]], Times[1.5, Power[1.5, 4]]], [Plus[1, ]]], Times[-1, Plus[2, , 2, 1.5, 1.5], Plus[48, Times[112, ], Times[92, Power[, 2]], Times[32, Power[, 3]], Times[4, Power[, 4]], Times[16, 2], Times[32, , 2], Times[20, Power[, 2], 2], Times[4, Power[, 3], 2], Times[-24, 1.5], Times[-76, , 1.5], Times[-88, Power[, 2], 1.5], Times[-44, Power[, 3], 1.5], Times[-8, Power[, 4], 1.5], Times[24, 2, 1.5], Times[52, , 2, 1.5], Times[36, Power[, 2], 2, 1.5], Times[8, Power[, 3], 2, 1.5], Times[40, 1.5], Times[64, , 1.5], Times[34, Power[, 2], 1.5], Times[6, Power[, 3], 1.5], Times[8, 2, 1.5], Times[8, , 2, 1.5], Times[2, Power[, 2], 2, 1.5], Times[-26, 1.5, 1.5], Times[-62, , 1.5, 1.5], Times[-48, Power[, 2], 1.5, 1.5], Times[-12, Power[, 3], 1.5, 1.5], Times[26, 2, 1.5, 1.5], Times[36, , 2, 1.5, 1.5], Times[12, Power[, 2], 2, 1.5, 1.5], Times[5, Power[1.5, 2]], Times[3, , Power[1.5, 2]], Times[3, 2, Power[1.5, 2]], Times[2, , 2, Power[1.5, 2]], Times[-9, 1.5, Power[1.5, 2]], Times[-15, , 1.5, Power[1.5, 2]], Times[-6, Power[, 2], 1.5, Power[1.5, 2]], Times[9, 2, 1.5, Power[1.5, 2]], Times[6, , 2, 1.5, Power[1.5, 2]], Times[-1, Power[1.5, 3]], Times[-1, , Power[1.5, 3]], Times[2, Power[1.5, 3]], Times[-1, 1.5, Power[1.5, 3]], Times[-1, , 1.5, Power[1.5, 3]], Times[2, 1.5, Power[1.5, 3]], Times[64, 1.5], Times[108, , 1.5], Times[58, Power[, 2], 1.5], Times[10, Power[, 3], 1.5], Times[16, 2, 1.5], Times[20, , 2, 1.5], Times[6, Power[, 2], 2, 1.5], Times[-26, 1.5, 1.5], Times[-62, , 1.5, 1.5], Times[-48, Power[, 2], 1.5, 1.5], Times[-12, Power[, 3], 1.5, 1.5], Times[26, 2, 1.5, 1.5], Times[36, , 2, 1.5, 1.5], Times[12, Power[, 2], 2, 1.5, 1.5], Times[36, 1.5, 1.5], Times[38, , 1.5, 1.5], Times[10, Power[, 2], 1.5, 1.5], Times[4, 2, 1.5, 1.5], Times[2, , 2, 1.5, 1.5], Times[-18, 1.5, 1.5, 1.5], Times[-30, , 1.5, 1.5, 1.5], Times[-12, Power[, 2], 1.5, 1.5, 1.5], Times[18, 2, 1.5, 1.5, 1.5], Times[12, , 2, 1.5, 1.5, 1.5], Times[3, Power[1.5, 2], 1.5], Times[, Power[1.5, 2], 1.5], Times[2, Power[1.5, 2], 1.5], Times[-3, 1.5, Power[1.5, 2], 1.5], Times[-3, , 1.5, Power[1.5, 2], 1.5], Times[3, 2, 1.5, Power[1.5, 2], 1.5], Times[31, Power[1.5, 2]], Times[35, , Power[1.5, 2]], Times[10, Power[, 2], Power[1.5, 2]], Times[2, Power[1.5, 2]], Times[-9, 1.5, Power[1.5, 2]], Times[-15, , 1.5, Power[1.5, 2]], Times[-6, Power[, 2], 1.5, Power[1.5, 2]], Times[9, 2, 1.5, Power[1.5, 2]], Times[6, , 2, 1.5, Power[1.5, 2]], Times[9, 1.5, Power[1.5, 2]], Times[5, , 1.5, Power[1.5, 2]], Times[-1, 2, 1.5, Power[1.5, 2]], Times[-3, 1.5, 1.5, Power[1.5, 2]], Times[-3, , 1.5, 1.5, Power[1.5, 2]], Times[3, 2, 1.5, 1.5, Power[1.5, 2]], Times[5, Power[1.5, 3]], Times[3, , Power[1.5, 3]], Times[-1, 2, Power[1.5, 3]], Times[-1, 1.5, Power[1.5, 3]], Times[-1, , 1.5, Power[1.5, 3]], Times[2, 1.5, Power[1.5, 3]]], [Plus[2, ]]], Times[2, Plus[2, ], Plus[2, , 1.5], Plus[2, Times[2, ], 1.5, 1.5], Plus[2, , 2, 1.5, 1.5], Plus[3, , 2, 1.5, 1.5], [Plus[3, ]]]], 0], Equal[[-1], 0], Equal[[0], Times[Rational[1, 2], Power[Plus[1, 2], -1], Power[1.5, -1], Power[Plus[1.5, 1.5], -1], Power[Plus[2, 1.5, 1.5], -1], Plus[1, 2, 1.5, 1.5], Plus[Times[Plus[1, 1.5, 1.5], Plus[Times[2, 1.5, 1.5], Power[1.5, 2], Times[1.5, Power[1.5, 2]], Times[2, 1.5, 1.5], Times[2, 1.5, 1.5, 1.5], Times[-1, Power[1.5, 2]], Times[1.5, Power[1.5, 2]]]], Times[-1, Plus[1.5, 1.5], Plus[1, 1.5, 1.5], Plus[1.5, Times[-1, 1.5], Times[1.5, Plus[2, 1.5, 1.5]]]]]]], Equal[[1], Plus[1, Times[Rational[1, 2], Power[Plus[1, 2], -1], Power[1.5, -1], Power[Plus[1.5, 1.5], -1], Power[Plus[2, 1.5, 1.5], -1], Plus[1, 2, 1.5, 1.5], Plus[Times[Plus[1, 1.5, 1.5], Plus[Times[2, 1.5, 1.5], Power[1.5, 2], Times[1.5, Power[1.5, 2]], Times[2, 1.5, 1.5], Times[2, 1.5, 1.5, 1.5], Times[-1, Power[1.5, 2]], Times[1.5, Power[1.5, 2]]]], Times[-1, Plus[1.5, 1.5], Plus[1, 1.5, 1.5], Plus[1.5, Times[-1, 1.5], Times[1.5, Plus[2, 1.5, 1.5]]]]]]]]}]][3.0]]]]], {Rule[n, 2], Rule[x, 1.5], Rule[α, 1.5], Rule[β, 1.5]} ... skip entries to safe data
18.18.E16	${\displaystyle{\displaystyle C^{(\mu)}_{n}\left(x\right)=\sum_{\ell=0}^{\left\lfloor n/2\right\rfloor}\frac{\lambda+n-2\ell}{\lambda}\frac{{\left(\mu\right)_{n-\ell}}}{{\left(\lambda+1\right)_{n-\ell}}}\frac{{\left(\mu-\lambda\right)_{\ell}}}{\ell!}C^{(\lambda)}_{n-2\ell}\left(x\right)}}$ \ultrasphpoly{\mu}{n}@{x} = \sum_{\ell=0}^{\floor{n/2}}\frac{\lambda+n-2\ell}{\lambda}\frac{\Pochhammersym{\mu}{n-\ell}}{\Pochhammersym{\lambda+1}{n-\ell}}\frac{\Pochhammersym{\mu-\lambda}{\ell}}{\ell!}\ultrasphpoly{\lambda}{n-2\ell}@{x}		GegenbauerC(n, mu, x) = sum((lambda + n - 2*ell)/(lambda)*(pochhammer(mu, n - ell))/(pochhammer(lambda + 1, n - ell))*(pochhammer(mu - lambda, ell))/(factorial(ell))*GegenbauerC(n - 2*ell, lambda, x), ell = 0..floor(n/2))	GegenbauerC[n, \[Mu], x] == Sum[Divide[\[Lambda]+ n - 2*\[ScriptL],\[Lambda]]*Divide[Pochhammer[\[Mu], n - \[ScriptL]],Pochhammer[\[Lambda]+ 1, n - \[ScriptL]]]*Divide[Pochhammer[\[Mu]- \[Lambda], \[ScriptL]],(\[ScriptL])!]*GegenbauerC[n - 2*\[ScriptL], \[Lambda], x], {\[ScriptL], 0, Floor[n/2]}, GenerateConditions->None]	Failure	Aborted	Successful [Tested: 300]	Failed [300 / 300] Result: Plus[Complex[2.598076211353316, 1.4999999999999998], Times[Complex[-0.8660254037844387, 0.49999999999999994], Plus[Times[-2.0, DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[Plus[-1, Times[-2, ], 1], Plus[Times[-2, ], 1], Plus[-3, Times[-2, ], 1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[-1, Times[-1, ], 1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[Times[-1, ], 1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[, Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[1, , Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], []], Times[Plus[1, , Times[-1, 1], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Plus[1, , Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[Times[-12, ], Times[-56, Power<syntaxhighlight lang=mathematica>Result: Plus[Complex[5.281088913245535, 5.647114317029973], Times[Complex[-0.8660254037844387, 0.49999999999999994], Plus[Times[-2.0, DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[Plus[-1, Times[-2, ], 2], Plus[Times[-2, ], 2], Plus[-3, Times[-2, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[-1, Times[-1, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[Times[-1, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[, Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[1, , Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], []], Times[Plus[1, , Times[-1, 2], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Plus[1, , Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[Times[-12, ], Times[-56, Power[, 2]], Times[-86, Power[, 3]], Times[-48, Power[, 4]], Times[-8, Power[, 5]], Times[34, , 2], Times[105, Power[, 2], 2], Times[88, Power[, 3], 2], Times[20, Power[, 4], 2], Times[-31, , Power[2, 2]], Times[-52, Power[, 2], Power[2, 2]], Times[-18, Power[, 3], Power[2, 2]], Times[10, , Power[2, 3]], Times[7, Power[, 2], Power[2, 3]], Times[-1, , Power[2, 4]], Times[24, , Power[1.5, 2]], Times[112, Power[, 2], Power[1.5, 2]], Times[184, Power[, 3], Power[1.5, 2]], Times[128, Power[, 4], Power[1.5, 2]], Times[32, Power[, 5], Power[1.5, 2]], Times[-68, , 2, Power[1.5, 2]], Times[-228, Power[, 2], 2, Power[1.5, 2]], Times[-240, Power[, 3], 2, Power[1.5, 2]], Times[-80, Power[, 4], 2, Power[1.5, 2]], Times[68, , Power[2, 2], Power[1.5, 2]], Times[144, Power[, 2], Power[2, 2], Power[1.5, 2]], Times[72, Power[, 3], Power[2, 2], Power[1.5, 2]], Times[-28, , Power[2, 3], Power[1.5, 2]], Times[-28, Power[, 2], Power[2, 3], Power[1.5, 2]], Times[4, , Power[2, 4], Power[1.5, 2]], Times[18, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[50, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[34, Power[, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[4, Power[, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-28, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-39, Power[, 2], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-8, Power[, 3], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-3, Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[3, , Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[Power[, 2], Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[4, Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[3, , Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-1, Power[2, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-44, , Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-140, Power[, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-144, Power[, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-48, Power[, 4], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[92, , 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[192, Power[, 2], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[96, Power[, 3], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-60, , Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-60, Power[, 2], Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[12, , Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[6, Power[, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[8, Power[, 3], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-3, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-10, , 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-12, Power[, 2], 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[5, Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[8, , Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-2, Power[2, 3], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[24, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[48, Power[, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[24, Power[, 3], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-36, , 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-36, Power[, 2], 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[12, , Power[2, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-2, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-4, Power[, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[4, , 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-1, Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-4, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-4, Power[, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[4, , 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[12, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[50, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[64, Power[, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[24, Power[, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-31, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-80, Power[, 2], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-44, Power[, 3], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[3, Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[32, , Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[30, Power[, 2], Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-4, Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-9, , Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[Power[2, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-24, , Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-88, Power[, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-96, Power[, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-32, Power[, 4], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, , 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[96, Power[, 2], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[48, Power[, 3], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-24, , Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-24, Power[, 2], Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[4, , Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-24, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-62, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-36, Power[, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[3, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[41, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, Power[, 2], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-5, Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-17, , Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, , Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[96, Power[, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[48, Power[, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-48, , 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-48, Power[, 2], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[12, , Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[8, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[12, Power[, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-1, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-8, , 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-24, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-24, Power[, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[12, , 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[4, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], [Plus[1, ]]], Times[-1, , Plus[1, , Times[-1, 2], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Plus[12, Times[44, ], Times[42, Power[, 2]], Times[-6, Power[, 3]], Times[-24, Power[, 4]], Times[-8, Power[, 5]], Times[-16, 2], Times[-23, , 2], Times[25, Power[, 2], 2], Times[52, Power[, 3], 2], Times[20, Power[, 4], 2], Power[2, 2], Times[-19, , Power[2, 2]], Times[-38, Power[, 2], Power[2, 2]], Times[-18, Power[, 3], Power[2, 2]], Times[4, Power[2, 3]], Times[11, , Power[2, 3]], Times[7, Power[, 2], Power[2, 3]], Times[-1, Power[2, 4]], Times[-1, , Power[2, 4]], Times[24, Power[1.5, 2]], Times[136, , Power[1.5, 2]], Times[296, Power[, 2], Power[1.5, 2]], Times[312, Power[, 3], Power[1.5, 2]], Times[160, Power[, 4], Power[1.5, 2]], Times[32, Power[, 5], Power[1.5, 2]], Times[-68, 2, Power[1.5, 2]], Times[-296, , 2, Power[1.5, 2]], Times[-468, Power[, 2], 2, Power[1.5, 2]], Times[-320, Power[, 3], 2, Power[1.5, 2]], Times[-80, Power[, 4], 2, Power[1.5, 2]], Times[68, Power[2, 2], Power[1.5, 2]], Times[212, , Power[2, 2], Power[1.5, 2]], Times[216, Power[, 2], Power[2, 2], Power[1.5, 2]], Times[72, Power[, 3], Power[2, 2], Power[1.5, 2]], Times[-28, Power[2, 3], Power[1.5, 2]], Times[-56, , Power[2, 3], Power[1.5, 2]], Times[-28, Power[, 2], Power[2, 3], Power[1.5, 2]], Times[4, Power[2, 4], Power[1.5, 2]], Times[4, , Power[2, 4], Power[1.5, 2]], Times[-10, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[14, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[98, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[110, Power[, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[36, Power[, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-20, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-123, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-175, Power[, 2], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-72, Power[, 3], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[39, Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[94, , Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[53, Power[, 2], Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-17, Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-17, , Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, Power[2, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-92, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-408, , Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-652, Power[, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-448, Power[, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-112, Power[, 4], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[204, 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[652, , 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[672, Power[, 2], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[224, Power[, 3], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-152, Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-312, , Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-156, Power[, 2], Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, , Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-4, Power[2, 4], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-18, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-102, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-140, Power[, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-56, Power[, 3], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[60, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[148, , 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[84, Power[, 2], 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-42, Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-44, , Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[8, Power[2, 3], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[136, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[440, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[456, Power[, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[152, Power[, 3], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-220, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-456, , 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-228, Power[, 2], 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[108, Power[2, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[108, , Power[2, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-16, Power[2, 3], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[22, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[60, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[36, Power[, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-32, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-36, , 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[10, Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-96, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-200, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-100, Power[, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[100, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[100, , 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-24, Power[2, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-6, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 4]], Times[-8, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 4]], Times[4, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 4]], Times[32, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 4]], Times[32, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 4]], Times[-16, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 4]], Times[-4, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 5]], Times[-24, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-106, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-162, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-104, Power[, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-24, Power[, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[53, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[165, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[164, Power[, 2], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[52, Power[, 3], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-42, Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-86, , Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-42, Power[, 2], Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[15, Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[15, , Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-2, Power[2, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[24, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[112, , Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[184, Power[, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[128, Power[, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[32, Power[, 4], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-68, 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-228, , 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-240, Power[, 2], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-80, Power[, 3], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[68, Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[144, , Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[72, Power[, 2], Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-28, Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-28, , Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[4, Power[2, 4], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[56, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[182, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[186, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[60, Power[, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-87, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-183, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-92, Power[, 2], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[45, Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[47, , Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-8, Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-68, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-228, , Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-240, Power[, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-80, Power[, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[136, 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[288, , 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[144, Power[, 2], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-84, Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-84, , Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[16, Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-42, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-92, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-48, Power[, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[40, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, , 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-10, Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[68, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[144, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[72, Power[, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-84, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-84, , 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[24, Power[2, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[10, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[12, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-4, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-28, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-28, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[16, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[4, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], [Plus[2, ]]], Times[, Plus[1, ], Plus[3, Times[2, ], Times[-1, 2], Times[-2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Plus[4, Times[2, ], Times[-1, 2], Times[-2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Plus[1, Times[2, ], Times[-1, 2], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Plus[1, , Times[-1, 2], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Plus[2, , Times[-1, 2], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], [Plus[3, ]]]], 0], Equal[[1], 0], Equal[[2], Times[-1, Plus[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Plus[-1, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], -1], GegenbauerC[Plus[-2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 1.5], Power[Pochhammer[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2], -1], Pochhammer[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]]], Equal[[3], Plus[Times[-1, Plus[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Plus[-1, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], -1], GegenbauerC[Plus[-2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 1.5], Power[Pochhammer[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2], -1], Pochhammer[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[Plus[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[Plus[-4, 2, Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], -1], Power[Plus[-3, 2, Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], -1], Power[Plus[2, Times[-1, 2], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], -1], Plus[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Plus[-1, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], -1], Plus[Times[-2, Plus[-2, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[-3, Times[4, 2], Times[-1, Power[2, 2]], Times[6, Power[1.5, 2]], Times[-8, 2, Power[1.5, 2]], Times[2, Power[2, 2], Power[1.5, 2]], Times[3, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-2, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-8, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[4, 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]]], GegenbauerC[Plus[-2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 1.5]], Times[Plus[-1, 2], 2, Plus[-3, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], GegenbauerC[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 1.5]]], Power[Pochhammer[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2], -1], Pochhammer[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]]]]}]][2.0]], Times[Complex[2.866025403784439, 0.49999999999999994], DifferenceRoot[Function[{, }, {Equal[Plus[Times[Plus[-1, Times[-2, ], 2], Plus[Times[-2, ], 2], Plus[-3, Times[-2, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[-1, Times[-1, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[Times[-1, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[, Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[1, , Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], []], Times[-1, Plus[-1, Times[-1, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[1, , Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[-12, Times[-68, ], Times[-148, Power[, 2]], Times[-150, Power[, 3]], Times[-64, Power[, 4]], Times[-8, Power[, 5]], Times[34, 2], Times[148, , 2], Times[225, Power[, 2], 2], Times[128, Power[, 3], 2], Times[20, Power[, 4], 2], Times[-34, Power[2, 2]], Times[-103, , Power[2, 2]], Times[-88, Power[, 2], Power[2, 2]], Times[-18, Power[, 3], Power[2, 2]], Times[14, Power[2, 3]], Times[24, , Power[2, 3]], Times[7, Power[, 2], Power[2, 3]], Times[-2, Power[2, 4]], Times[-1, , 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Rational[1, 6]], Pi]]], Times[58, Power[, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[4, Power[, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-40, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-118, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-87, Power[, 2], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-8, Power[, 3], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[25, Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[33, , Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[Power[, 2], Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-2, Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[3, , Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-1, Power[2, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-44, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-184, , Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-284, Power[, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-192, Power[, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-48, Power[, 4], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[92, 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[284, , 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[288, Power[, 2], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[96, Power[, 3], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-60, Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-120, , Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-60, Power[, 2], Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[12, Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[12, , Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-6, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-14, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-2, Power[, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[8, Power[, 3], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[7, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[2, , 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-12, Power[, 2], 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[8, , Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-2, Power[2, 3], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[24, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[72, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[72, Power[, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[24, Power[, 3], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-36, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-72, , 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-36, Power[, 2], 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[12, Power[2, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[12, , Power[2, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-2, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-4, Power[, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[4, , 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-1, Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-4, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-8, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-4, Power[, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[4, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[4, , 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[12, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[56, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[98, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[80, Power[, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[24, Power[, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-22, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-79, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-104, Power[, 2], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-44, Power[, 3], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[15, Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, , Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[30, Power[, 2], Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-6, Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-9, , Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[Power[2, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-24, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-112, , Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-184, Power[, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-128, Power[, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-32, Power[, 4], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[140, , 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[144, Power[, 2], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[48, Power[, 3], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-24, Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-48, , Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-24, Power[, 2], Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[4, Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[4, , Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-18, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-68, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-86, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-36, Power[, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[25, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[65, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, Power[, 2], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-11, Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-17, , Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[140, , Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[144, Power[, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[48, Power[, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-48, 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-96, , 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-48, Power[, 2], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[12, Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[12, , Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[6, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[16, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[12, Power[, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-5, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-8, , 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-24, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-48, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-24, Power[, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[12, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[12, , 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[4, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[4, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], [Plus[1, ]]], Times[Plus[1, ], Plus[-1, Times[-1, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[36, Times[132, ], Times[144, Power[, 2]], Times[42, Power[, 3]], Times[-16, Power[, 4]], Times[-8, Power[, 5]], Times[-66, 2], Times[-144, , 2], Times[-63, Power[, 2], 2], Times[32, Power[, 3], 2], Times[20, Power[, 4], 2], Times[36, Power[2, 2]], Times[33, , Power[2, 2]], Times[-20, Power[, 2], Power[2, 2]], Times[-18, Power[, 3], Power[2, 2]], Times[-6, Power[2, 3]], Times[4, , Power[2, 3]], Times[7, Power[, 2], Power[2, 3]], Times[-1, , Power[2, 4]], Times[24, Power[1.5, 2]], Times[136, , Power[1.5, 2]], Times[296, Power[, 2], Power[1.5, 2]], Times[312, Power[, 3], Power[1.5, 2]], Times[160, Power[, 4], Power[1.5, 2]], Times[32, Power[, 5], Power[1.5, 2]], Times[-68, 2, Power[1.5, 2]], Times[-296, , 2, Power[1.5, 2]], Times[-468, Power[, 2], 2, Power[1.5, 2]], Times[-320, Power[, 3], 2, Power[1.5, 2]], Times[-80, Power[, 4], 2, Power[1.5, 2]], Times[68, Power[2, 2], Power[1.5, 2]], Times[212, , Power[2, 2], Power[1.5, 2]], Times[216, Power[, 2], Power[2, 2], Power[1.5, 2]], Times[72, Power[, 3], Power[2, 2], Power[1.5, 2]], Times[-28, Power[2, 3], Power[1.5, 2]], Times[-56, , Power[2, 3], Power[1.5, 2]], Times[-28, Power[, 2], Power[2, 3], Power[1.5, 2]], Times[4, Power[2, 4], Power[1.5, 2]], Times[4, , Power[2, 4], Power[1.5, 2]], Times[-62, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-112, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[8, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[90, Power[, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[36, Power[, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[56, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-8, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-135, Power[, 2], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-72, Power[, 3], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[4, Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[69, , Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[53, Power[, 2], Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-12, Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-17, , Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, Power[2, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-92, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-408, , Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-652, Power[, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-448, Power[, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-112, Power[, 4], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[204, 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[652, , 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[672, Power[, 2], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[224, Power[, 3], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-152, Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-312, , Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-156, Power[, 2], Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, , Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-4, Power[2, 4], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[18, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-52, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-124, Power[, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-56, Power[, 3], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[26, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[124, , 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[84, Power[, 2], 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-34, Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-44, , Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[8, Power[2, 3], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[136, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[440, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[456, Power[, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[152, Power[, 3], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-220, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-456, , 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-228, Power[, 2], 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[108, Power[2, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[108, , Power[2, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-16, Power[2, 3], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[14, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[56, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[36, Power[, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-28, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-36, , 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[10, Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-96, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-200, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-100, Power[, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[100, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[100, , 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-24, Power[2, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-6, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 4]], Times[-8, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 4]], Times[4, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 4]], Times[32, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 4]], Times[32, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 4]], Times[-16, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 4]], Times[-4, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 5]], Times[-36, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-144, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-194, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-112, Power[, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-24, Power[, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[72, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[197, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[176, Power[, 2], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[52, Power[, 3], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-50, Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-92, , Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-42, Power[, 2], Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[16, Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[15, , Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-2, Power[2, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[24, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[112, , Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[184, Power[, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[128, Power[, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[32, Power[, 4], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-68, 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-228, , 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-240, Power[, 2], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-80, Power[, 3], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[68, Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[144, , Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[72, Power[, 2], Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-28, Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-28, , Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[4, Power[2, 4], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[82, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[232, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[206, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[60, Power[, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-112, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-203, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-92, Power[, 2], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[50, Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[47, , Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-8, Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-68, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-228, , Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-240, Power[, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-80, Power[, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[136, 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[288, , 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[144, Power[, 2], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-84, Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-84, , Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[16, Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-60, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-108, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-48, Power[, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[48, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, , 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-10, Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[68, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[144, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[72, Power[, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-84, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-84, , 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[24, Power[2, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[14, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[12, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-4, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-28, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-28, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[16, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[4, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], [Plus[2, ]]], Times[-1, Plus[1, ], Plus[2, ], Plus[-1, Times[-2, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[-4, Times[-2, ], 2, Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Plus[-3, Times[-2, ], 2, Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Plus[-2, Times[-1, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[-1, Times[-1, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], Times[GegenbauerC[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 1.5], Power[Pochhammer[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2], -1], Pochhammer[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]]], Equal[[2], Plus[Times[-1, Plus[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Plus[-1, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], -1], GegenbauerC[Plus[-2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 1.5], Power[Pochhammer[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2], -1], Pochhammer[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[GegenbauerC[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 1.5], Power[Pochhammer[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2], -1], Pochhammer[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]]]]}]][2.0]]]]], {Rule[n, 2], Rule[x, 1.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.18.E17	${\displaystyle{\displaystyle(2x)^{n}=n!\sum_{\ell=0}^{\left\lfloor n/2\right\rfloor}\frac{\lambda+n-2\ell}{\lambda}\frac{1}{{\left(\lambda+1\right)_{n-\ell}}\,\ell!}C^{(\lambda)}_{n-2\ell}\left(x\right)}}$ (2x)^{n} = n!\sum_{\ell=0}^{\floor{n/2}}\frac{\lambda+n-2\ell}{\lambda}\frac{1}{\Pochhammersym{\lambda+1}{n-\ell}\,\ell!}\ultrasphpoly{\lambda}{n-2\ell}@{x}		(2*x)^(n) = factorial(n)*sum((lambda + n - 2*ell)/(lambda)*(1)/(pochhammer(lambda + 1, n - ell)*factorial(ell))*GegenbauerC(n - 2*ell, lambda, x), ell = 0..floor(n/2))	(2*x)^(n) == (n)!*Sum[Divide[\[Lambda]+ n - 2*\[ScriptL],\[Lambda]]*Divide[1,Pochhammer[\[Lambda]+ 1, n - \[ScriptL]]*(\[ScriptL])!]*GegenbauerC[n - 2*\[ScriptL], \[Lambda], x], {\[ScriptL], 0, Floor[n/2]}, GenerateConditions->None]	Failure	Aborted	Error	Failed [74 / 90] Result: Plus[3.0, Times[Complex[-0.8660254037844387, 0.49999999999999994], Plus[Times[-2.0, DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[Plus[-1, Times[-2, ], 1], Plus[Times[-2, ], 1], Plus[-3, Times[-2, ], 1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[-1, Times[-1, ], 1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[Times[-1, ], 1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], []], Times[-1, Plus[-1, Times[-1, ], 1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[Times[12, ], Times[50, Power[, 2]], Times[64, Power[, 3]], Times[24, Power[, 4]], Times[-31, , 1], Times[-80, Power[, 2], 1], Times[-44, Power[, 3], 1], Times[3, Power[1, 2]], Times[32, , Power[1, 2]], Times[30, Power[, 2], Power[1, 2]], Times[-4, Power[1, 3]], Times[-9, , Power[1, 3]], Power[1, 4], Times[-24, , Power[1.5, 2]], Times[-88, Power[, 2], Power[1.5, 2]], Times[-96, Power[, 3], Power[1.5, 2]], Times[-32, Power[,<syntaxhighlight lang=mathematica>Result: Plus[9.0, Times[Complex[-1.7320508075688774, 0.9999999999999999], Plus[Times[-2.0, DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[Plus[-1, Times[-2, ], 2], Plus[Times[-2, ], 2], Plus[-3, Times[-2, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[-1, Times[-1, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[Times[-1, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], []], Times[-1, Plus[-1, Times[-1, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[Times[12, ], Times[50, Power[, 2]], Times[64, Power[, 3]], Times[24, Power[, 4]], Times[-31, , 2], Times[-80, Power[, 2], 2], Times[-44, Power[, 3], 2], Times[3, Power[2, 2]], Times[32, , Power[2, 2]], Times[30, Power[, 2], Power[2, 2]], Times[-4, Power[2, 3]], Times[-9, , Power[2, 3]], Power[2, 4], Times[-24, , Power[1.5, 2]], Times[-88, Power[, 2], Power[1.5, 2]], Times[-96, Power[, 3], Power[1.5, 2]], Times[-32, Power[, 4], Power[1.5, 2]], Times[44, , 2, Power[1.5, 2]], Times[96, Power[, 2], 2, Power[1.5, 2]], Times[48, Power[, 3], 2, Power[1.5, 2]], Times[-24, , Power[2, 2], Power[1.5, 2]], Times[-24, Power[, 2], Power[2, 2], Power[1.5, 2]], Times[4, , Power[2, 3], Power[1.5, 2]], Times[-24, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-62, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-36, Power[, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[3, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[41, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, Power[, 2], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-5, Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-17, , Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, , Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[96, Power[, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[48, Power[, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-48, , 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-48, Power[, 2], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[12, , Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[8, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[12, Power[, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-1, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-8, , 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-24, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-24, Power[, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[12, , 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[4, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]]], [Plus[1, ]]], Times[, Plus[-24, Times[-106, ], Times[-162, Power[, 2]], Times[-104, Power[, 3]], Times[-24, Power[, 4]], Times[53, 2], Times[165, , 2], Times[164, Power[, 2], 2], Times[52, Power[, 3], 2], Times[-42, Power[2, 2]], Times[-86, , Power[2, 2]], Times[-42, Power[, 2], Power[2, 2]], Times[15, Power[2, 3]], Times[15, , Power[2, 3]], Times[-2, Power[2, 4]], Times[24, Power[1.5, 2]], Times[112, , Power[1.5, 2]], Times[184, Power[, 2], Power[1.5, 2]], Times[128, Power[, 3], Power[1.5, 2]], Times[32, Power[, 4], Power[1.5, 2]], Times[-68, 2, Power[1.5, 2]], Times[-228, , 2, Power[1.5, 2]], Times[-240, Power[, 2], 2, Power[1.5, 2]], Times[-80, Power[, 3], 2, Power[1.5, 2]], Times[68, Power[2, 2], Power[1.5, 2]], Times[144, , Power[2, 2], Power[1.5, 2]], Times[72, Power[, 2], Power[2, 2], Power[1.5, 2]], Times[-28, Power[2, 3], Power[1.5, 2]], Times[-28, , Power[2, 3], Power[1.5, 2]], Times[4, Power[2, 4], Power[1.5, 2]], Times[56, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[182, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[186, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[60, Power[, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-87, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-183, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-92, Power[, 2], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[45, Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[47, , Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-8, Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-68, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-228, , Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-240, Power[, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-80, Power[, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[136, 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[288, , 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[144, Power[, 2], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-84, Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-84, , Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[16, Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-42, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-92, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-48, Power[, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[40, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[44, , 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-10, Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[68, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[144, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[72, Power[, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-84, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-84, , 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[24, Power[2, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[10, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[12, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-4, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-28, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-28, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[16, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[4, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 4]]], [Plus[2, ]]], Times[, Plus[1, ], Plus[3, Times[2, ], Times[-1, 2], Times[-2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Plus[4, Times[2, ], Times[-1, 2], Times[-2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Plus[1, Times[2, ], Times[-1, 2], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], [Plus[3, ]]]], 0], Equal[[1], 0], Equal[[2], Times[-1, Plus[Times[-1, 2], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], GegenbauerC[Plus[-2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 1.5], Power[Pochhammer[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2], -1]]], Equal[[3], Plus[Times[-1, Plus[Times[-1, 2], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], GegenbauerC[Plus[-2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 1.5], Power[Pochhammer[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2], -1]], Times[Plus[Times[-1, 2], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Plus[-4, 2, Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], -1], Power[Plus[-3, 2, Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], -1], Plus[Times[-2, Plus[-2, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[-3, Times[4, 2], Times[-1, Power[2, 2]], Times[6, Power[1.5, 2]], Times[-8, 2, Power[1.5, 2]], Times[2, Power[2, 2], Power[1.5, 2]], Times[3, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-2, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-8, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[4, 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]]], GegenbauerC[Plus[-2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 1.5]], Times[Plus[-1, 2], 2, Plus[-3, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], GegenbauerC[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 1.5]]], Power[Pochhammer[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2], -1]]]]}]][2.0]], Times[Complex[2.866025403784439, 0.49999999999999994], DifferenceRoot[Function[{, }, {Equal[Plus[Times[Plus[-1, Times[-2, ], 2], Plus[Times[-2, ], 2], Plus[-3, Times[-2, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[-1, Times[-1, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[Times[-1, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], []], Times[-1, Plus[-1, Times[-1, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[12, Times[56, ], Times[98, Power[, 2]], Times[80, Power[, 3]], Times[24, Power[, 4]], Times[-22, 2], Times[-79, , 2], Times[-104, Power[, 2], 2], Times[-44, Power[, 3], 2], Times[15, Power[2, 2]], Times[44, , Power[2, 2]], Times[30, Power[, 2], Power[2, 2]], Times[-6, Power[2, 3]], Times[-9, , Power[2, 3]], Power[2, 4], Times[-24, Power[1.5, 2]], Times[-112, , Power[1.5, 2]], Times[-184, Power[, 2], Power[1.5, 2]], Times[-128, Power[, 3], Power[1.5, 2]], Times[-32, Power[, 4], Power[1.5, 2]], Times[44, 2, Power[1.5, 2]], Times[140, , 2, Power[1.5, 2]], Times[144, Power[, 2], 2, Power[1.5, 2]], Times[48, Power[, 3], 2, Power[1.5, 2]], Times[-24, Power[2, 2], Power[1.5, 2]], Times[-48, , Power[2, 2], Power[1.5, 2]], Times[-24, Power[, 2], Power[2, 2], Power[1.5, 2]], Times[4, Power[2, 3], Power[1.5, 2]], Times[4, , Power[2, 3], Power[1.5, 2]], Times[-18, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-68, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-86, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-36, Power[, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[25, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[65, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, Power[, 2], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-11, Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-17, , Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[44, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[140, , Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[144, Power[, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[48, Power[, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-48, 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-96, , 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-48, Power[, 2], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[12, Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[12, , Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[6, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[16, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[12, Power[, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-5, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-8, , 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-24, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-48, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-24, Power[, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[12, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[12, , 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[4, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[4, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]]], [Plus[1, ]]], Times[Plus[1, ], Plus[-36, Times[-144, ], Times[-194, Power[, 2]], Times[-112, Power[, 3]], Times[-24, Power[, 4]], Times[72, 2], Times[197, , 2], Times[176, Power[, 2], 2], Times[52, Power[, 3], 2], Times[-50, Power[2, 2]], Times[-92, , Power[2, 2]], Times[-42, Power[, 2], Power[2, 2]], Times[16, Power[2, 3]], Times[15, , Power[2, 3]], Times[-2, Power[2, 4]], Times[24, Power[1.5, 2]], Times[112, , Power[1.5, 2]], Times[184, Power[, 2], Power[1.5, 2]], Times[128, Power[, 3], Power[1.5, 2]], Times[32, Power[, 4], Power[1.5, 2]], Times[-68, 2, Power[1.5, 2]], Times[-228, , 2, Power[1.5, 2]], Times[-240, Power[, 2], 2, Power[1.5, 2]], Times[-80, Power[, 3], 2, Power[1.5, 2]], Times[68, Power[2, 2], Power[1.5, 2]], Times[144, , Power[2, 2], Power[1.5, 2]], Times[72, Power[, 2], Power[2, 2], Power[1.5, 2]], Times[-28, Power[2, 3], Power[1.5, 2]], Times[-28, , Power[2, 3], Power[1.5, 2]], Times[4, Power[2, 4], Power[1.5, 2]], Times[82, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[232, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[206, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[60, Power[, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-112, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-203, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-92, Power[, 2], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[50, Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[47, , Power[2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-8, Power[2, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-68, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-228, , Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-240, Power[, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-80, Power[, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[136, 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[288, , 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[144, Power[, 2], 2, Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-84, Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-84, , Power[2, 2], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[16, Power[2, 3], Power[1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-60, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-108, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-48, Power[, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[48, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[44, , 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-10, Power[2, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[68, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[144, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[72, Power[, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-84, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-84, , 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[24, Power[2, 2], Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[14, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[12, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-4, 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-28, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[-28, , Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[16, 2, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 3]], Times[4, Power[1.5, 2], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 4]]], [Plus[2, ]]], Times[-1, Plus[1, ], Plus[2, ], Plus[-1, Times[-2, ], 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Plus[-4, Times[-2, ], 2, Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Plus[-3, Times[-2, ], 2, Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], Times[GegenbauerC[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 1.5], Power[Pochhammer[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2], -1]]], Equal[[2], Plus[Times[-1, Plus[Times[-1, 2], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], GegenbauerC[Plus[-2, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 1.5], Power[Pochhammer[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2], -1]], Times[GegenbauerC[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 1.5], Power[Pochhammer[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2], -1]]]]}]][2.0]]]]], {Rule[n, 2], Rule[x, 1.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.18.E18	${\displaystyle{\displaystyle L^{(\beta)}_{n}\left(x\right)=\sum_{\ell=0}^{n}\frac{{\left(\beta-\alpha\right)_{n-\ell}}}{(n-\ell)!}L^{(\alpha)}_{\ell}\left(x\right)}}$ \LaguerrepolyL[\beta]{n}@{x} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\beta-\alpha}{n-\ell}}{(n-\ell)!}\LaguerrepolyL[\alpha]{\ell}@{x}		LaguerreL(n, beta, x) = sum((pochhammer(beta - alpha, n - ell))/(factorial(n - ell))*LaguerreL(ell, alpha, x), ell = 0..n)	LaguerreL[n, \[Beta], x] == Sum[Divide[Pochhammer[\[Beta]- \[Alpha], n - \[ScriptL]],(n - \[ScriptL])!]*LaguerreL[\[ScriptL], \[Alpha], x], {\[ScriptL], 0, n}, GenerateConditions->None]	Missing Macro Error	Failure	-	Failed [78 / 81] Result: Plus[1.0, Times[-1.0, DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[Plus[Times[-1, ], 1], Plus[, Times[-1, 1.5], 1.5], Plus[1, , Times[-1, 1.5], 1.5], []], Times[-1, Plus[1, , Times[-1, 1.5], 1.5], Plus[-1, Times[-3, ], Times[-3, Power[, 2]], Times[2, 1], Times[3, , 1], Times[-1, 1.5], Times[-1, , 1.5], 1.5, Times[2, , 1.5], Times[-1, 1, 1.5], Times[-1, , 1.5], Times[1, 1.5]], [Plus[1, ]]], Times[Plus[1, ], Plus[-3, Times[-6, ], Times[-3, Power[, 2]], Times[4, 1], Times[3, , 1], Times[-1, 1.5], Times[-1, , 1.5], Times[4, 1.5], Times[4, , 1.5], Times[-2, 1, 1.5], Times[1.5, 1.5], Times[-1, Power[1.5, 2]], Times[-1, 1.5], Times[-2, , 1.5], Times[2, 1, 1.5], Times[-1, 1.5, 1.5], Times[1.5, 1.5]], [Plus[2, ]]], Times[-1, Plus[1, ], Plus[2, ], Plus[-1, Times[-1, ], 1, 1.5], [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], LaguerreL[1, 1.5, 1.5]], Equal[[2], Plus[Times[Plus[Times[-1, 1.5], 1.5], LaguerreL[Pl<syntaxhighlight lang=mathematica>Result: Plus[0.25, Times[-1.0, DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[Plus[Times[-1, ], 2], Plus[, Times[-1, 1.5], 1.5], Plus[1, , Times[-1, 1.5], 1.5], []], Times[-1, Plus[1, , Times[-1, 1.5], 1.5], Plus[-1, Times[-3, ], Times[-3, Power[, 2]], Times[2, 2], Times[3, , 2], Times[-1, 1.5], Times[-1, , 1.5], 1.5, Times[2, , 1.5], Times[-1, 2, 1.5], Times[-1, , 1.5], Times[2, 1.5]], [Plus[1, ]]], Times[Plus[1, ], Plus[-3, Times[-6, ], Times[-3, Power[, 2]], Times[4, 2], Times[3, , 2], Times[-1, 1.5], Times[-1, , 1.5], Times[4, 1.5], Times[4, , 1.5], Times[-2, 2, 1.5], Times[1.5, 1.5], Times[-1, Power[1.5, 2]], Times[-1, 1.5], Times[-2, , 1.5], Times[2, 2, 1.5], Times[-1, 1.5, 1.5], Times[1.5, 1.5]], [Plus[2, ]]], Times[-1, Plus[1, ], Plus[2, ], Plus[-1, Times[-1, ], 2, 1.5], [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], LaguerreL[2, 1.5, 1.5]], Equal[[2], Plus[Times[Plus[Times[-1, 1.5], 1.5], LaguerreL[Plus[-1, 2], 1.5, 1.5]], LaguerreL[2, 1.5, 1.5]]]}]][3.0]]], {Rule[n, 2], Rule[x, 1.5], Rule[α, 1.5], Rule[β, 1.5]} ... skip entries to safe data
18.18.E19	${\displaystyle{\displaystyle x^{n}={\left(\alpha+1\right)_{n}}\sum_{\ell=0}^{n}\frac{{\left(-n\right)_{\ell}}}{{\left(\alpha+1\right)_{\ell}}}L^{(\alpha)}_{\ell}\left(x\right)}}$ x^{n} = \Pochhammersym{\alpha+1}{n}\sum_{\ell=0}^{n}\frac{\Pochhammersym{-n}{\ell}}{\Pochhammersym{\alpha+1}{\ell}}\LaguerrepolyL[\alpha]{\ell}@{x}		(x)^(n) = pochhammer(alpha + 1, n)*sum((pochhammer(- n, ell))/(pochhammer(alpha + 1, ell))*LaguerreL(ell, alpha, x), ell = 0..n)	(x)^(n) == Pochhammer[\[Alpha]+ 1, n]*Sum[Divide[Pochhammer[- n, \[ScriptL]],Pochhammer[\[Alpha]+ 1, \[ScriptL]]]*LaguerreL[\[ScriptL], \[Alpha], x], {\[ScriptL], 0, n}, GenerateConditions->None]	Missing Macro Error	Failure	-	Failed [24 / 27] Result: Plus[1.5, Times[-2.5, DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[-1, Plus[-1, Times[-1, ], 1], Plus[Times[-1, ], 1], []], Times[Plus[-1, Times[-1, ], 1], Plus[-3, Times[-3, ], 1, 1.5, Times[-1, 1.5]], [Plus[1, ]]], Times[Plus[-7, Times[-9, ], Times[-3, Power[, 2]], Times[3, 1], Times[2, , 1], 1.5, Times[, 1.5], Times[-1, 1, 1.5], Times[-3, 1.5], Times[-2, , 1.5], Times[1, 1.5]], [Plus[2, ]]], Times[Plus[2, ], Plus[2, , 1.5], [Plus[3, ]]]], 0], Equal[[-1], 0], Equal[[0], 0], Equal[[1], 1]}]][2.0]]], {Rule[n, 1], Rule[x, 1.5], Rule[α, 1.5]} Result: Plus[2.25, Times[-8.75, DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[-1, Plus[-1, Times[-1, ], 2], Plus[Times[-1, ], 2], []], Times[Plus[-1, Times[-1, ], 2], Plus[-3, Times[-3, ], 2, 1.5, Times[-1, 1.5]], [Plus[1, ]]], Times[Plus[-7, Times[-9, ], Times[-3, Power[, 2]], Times[3, 2], Times[2, , 2], 1.5, Times[, 1.5], Times[-1, 2, 1.5], Times[-3, 1.5], Times[-2, , 1.5], Times[2, 1.5]], [Plus[2, ]]], Times[Plus[2, ], Plus[2, , 1.5], [Plus[3, ]]]], 0], Equal[[-1], 0], Equal[[0], 0], Equal[[1], 1]}]][3.0]]], {Rule[n, 2], Rule[x, 1.5], Rule[α, 1.5]} ... skip entries to safe data
18.18.E20	${\displaystyle{\displaystyle(2x)^{n}=\sum_{\ell=0}^{\left\lfloor n/2\right\rfloor}\frac{{\left(-n\right)_{2\ell}}}{\ell!}H_{n-2\ell}\left(x\right)}}$ (2x)^{n} = \sum_{\ell=0}^{\floor{n/2}}\frac{\Pochhammersym{-n}{2\ell}}{\ell!}\HermitepolyH{n-2\ell}@{x}		(2*x)^(n) = sum((pochhammer(- n, 2*ell))/(factorial(ell))*HermiteH(n - 2*ell, x), ell = 0..floor(n/2))	(2*x)^(n) == Sum[Divide[Pochhammer[- n, 2*\[ScriptL]],(\[ScriptL])!]*HermiteH[n - 2*\[ScriptL], x], {\[ScriptL], 0, Floor[n/2]}, GenerateConditions->None]	Failure	Failure	Successful [Tested: 9]	Failed [9 / 9] Result: 3.0 Test Values: {Rule[n, 1], Rule[x, 1.5]} Result: 9.0 Test Values: {Rule[n, 2], Rule[x, 1.5]} ... skip entries to safe data
18.18.E21	${\displaystyle{\displaystyle T_{m}\left(x\right)T_{n}\left(x\right)=\tfrac{1}{2}(T_{m+n}\left(x\right)+T_{m-n}\left(x\right))}}$ \ChebyshevpolyT{m}@{x}\ChebyshevpolyT{n}@{x} = \tfrac{1}{2}(\ChebyshevpolyT{m+n}@{x}+\ChebyshevpolyT{m-n}@{x})		ChebyshevT(m, x)*ChebyshevT(n, x) = (1)/(2)*(ChebyshevT(m + n, x)+ ChebyshevT(m - n, x))	ChebyshevT[m, x]*ChebyshevT[n, x] == Divide[1,2]*(ChebyshevT[m + n, x]+ ChebyshevT[m - n, x])	Failure	Failure	Successful [Tested: 27]	Successful [Tested: 27]
18.18.E24	${\displaystyle{\displaystyle b_{n,\ell}=\genfrac{(}{)}{0.0pt}{}{n}{\ell}\frac{{\left(n+\alpha+\beta+1\right)_{\ell}}{\left(-\beta-n\right)_{n-\ell}}}{2^{\ell}{\left(\alpha+1\right)_{n}}}}}$ b_{n,\ell} = \binom{n}{\ell}\frac{\Pochhammersym{n+\alpha+\beta+1}{\ell}\Pochhammersym{-\beta-n}{n-\ell}}{2^{\ell}\Pochhammersym{\alpha+1}{n}}		b[n , ell] = binomial(n,ell)*(pochhammer(n + alpha + beta + 1, ell)*pochhammer(- beta - n, n - ell))/((2)^(ell)* pochhammer(alpha + 1, n))	Subscript[b, n , \[ScriptL]] == Binomial[n,\[ScriptL]]*Divide[Pochhammer[n + \[Alpha]+ \[Beta]+ 1, \[ScriptL]]*Pochhammer[- \[Beta]- n, n - \[ScriptL]],(2)^\[ScriptL]* Pochhammer[\[Alpha]+ 1, n]]	Failure	Failure	Error	Failed [270 / 270] Result: Plus[Complex[0.8660254037844387, 0.49999999999999994], Times[-0.4, Power[2.0, Times[-1.0, ℓ]], Binomial[1.0, ℓ], Pochhammer[-2.5, Plus[1.0, Times[-1.0, ℓ]]], Pochhammer[5.0, ℓ]]] Test Values: {Rule[n, 1], Rule[α, 1.5], Rule[β, 1.5], Rule[Subscript[b, n, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Plus[Complex[0.8660254037844387, 0.49999999999999994], Times[-0.11428571428571428, Power[2.0, Times[-1.0, ℓ]], Binomial[2.0, ℓ], Pochhammer[-3.5, Plus[2.0, Times[-1.0, ℓ]]], Pochhammer[6.0, ℓ]]] Test Values: {Rule[n, 2], Rule[α, 1.5], Rule[β, 1.5], Rule[Subscript[b, n, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.18.E25	${\displaystyle{\displaystyle\frac{P^{(\alpha,\beta)}_{n}\left(x\right)}{P^{(\alpha,\beta)}_{n}\left(1\right)}\frac{P^{(\alpha,\beta)}_{n}\left(y\right)}{P^{(\alpha,\beta)}_{n}\left(1\right)}=\sum_{\ell=0}^{n}b_{n,\ell}(x+y)^{\ell}\*\frac{P^{(\alpha,\beta)}_{\ell}\left(\ifrac{(1+xy)}{(x+y)}\right)}{P^{(\alpha,\beta)}_{\ell}\left(1\right)}}}$ \frac{\JacobipolyP{\alpha}{\beta}{n}@{x}}{\JacobipolyP{\alpha}{\beta}{n}@{1}}\frac{\JacobipolyP{\alpha}{\beta}{n}@{y}}{\JacobipolyP{\alpha}{\beta}{n}@{1}} = \sum_{\ell=0}^{n}b_{n,\ell}(x+y)^{\ell}\*\frac{\JacobipolyP{\alpha}{\beta}{\ell}@{\ifrac{(1+xy)}{(x+y)}}}{\JacobipolyP{\alpha}{\beta}{\ell}@{1}}		(JacobiP(n, alpha, beta, x))/(JacobiP(n, alpha, beta, 1))*(JacobiP(n, alpha, beta, y))/(JacobiP(n, alpha, beta, 1)) = sum(b[n , ell]*(x + y)^(ell)*(JacobiP(ell, alpha, beta, (1 + x*y)/(x + y)))/(JacobiP(ell, alpha, beta, 1)), ell = 0..n)	Divide[JacobiP[n, \[Alpha], \[Beta], x],JacobiP[n, \[Alpha], \[Beta], 1]]*Divide[JacobiP[n, \[Alpha], \[Beta], y],JacobiP[n, \[Alpha], \[Beta], 1]] == Sum[Subscript[b, n , \[ScriptL]]*(x + y)^\[ScriptL]*Divide[JacobiP[\[ScriptL], \[Alpha], \[Beta], Divide[1 + x*y,x + y]],JacobiP[\[ScriptL], \[Alpha], \[Beta], 1]], {\[ScriptL], 0, n}, GenerateConditions->None]	Failure	Failure	Error	Skipped - Because timed out
18.18.E26	${\displaystyle{\displaystyle\frac{P^{(\alpha,\beta)}_{n}\left(x\right)}{P^{(\alpha,\beta)}_{n}\left(1\right)}=\sum_{\ell=0}^{n}b_{n,\ell}(x+1)^{\ell}}}$ \frac{\JacobipolyP{\alpha}{\beta}{n}@{x}}{\JacobipolyP{\alpha}{\beta}{n}@{1}} = \sum_{\ell=0}^{n}b_{n,\ell}(x+1)^{\ell}		(JacobiP(n, alpha, beta, x))/(JacobiP(n, alpha, beta, 1)) = sum(b[n , ell]*(x + 1)^(ell), ell = 0..n)	Divide[JacobiP[n, \[Alpha], \[Beta], x],JacobiP[n, \[Alpha], \[Beta], 1]] == Sum[Subscript[b, n , \[ScriptL]]*(x + 1)^\[ScriptL], {\[ScriptL], 0, n}, GenerateConditions->None]	Failure	Failure	Failed [299 / 300] Result: -1.531088914-1.750000000*I Test Values: {alpha = 3/2, beta = 3/2, x = 3/2, b[n,ell] = 1/2*3^(1/2)+1/2*I, n = 1} Result: -5.943747689-4.875000000*I Test Values: {alpha = 3/2, beta = 3/2, x = 3/2, b[n,ell] = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [299 / 300] Result: Complex[-1.5310889132455356, -1.7499999999999998] Test Values: {Rule[n, 1], Rule[x, Rational[3, 2]], Rule[α, Rational[3, 2]], Rule[β, Rational[3, 2]], Rule[Subscript[b, n, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-5.943747686898277, -4.874999999999999] Test Values: {Rule[n, 2], Rule[x, Rational[3, 2]], Rule[α, Rational[3, 2]], Rule[β, Rational[3, 2]], Rule[Subscript[b, n, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.18.E27	${\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{n!\,L^{(\alpha)}_{n}\left(x\right)L^{(\alpha)}_{n}\left(y\right)}{{\left(\alpha+1\right)_{n}}}z^{n}=\frac{\Gamma\left(\alpha+1\right)(xyz)^{-\frac{1}{2}\alpha}}{1-z}\*\exp\left(\frac{-(x+y)z}{1-z}\right)I_{\alpha}\left(\frac{2(xyz)^{\frac{1}{2}}}{1-z}\right)}}$ \sum_{n=0}^{\infty}\frac{n!\,\LaguerrepolyL[\alpha]{n}@{x}\LaguerrepolyL[\alpha]{n}@{y}}{\Pochhammersym{\alpha+1}{n}}z^{n} = \frac{\EulerGamma@{\alpha+1}(xyz)^{-\frac{1}{2}\alpha}}{1-z}\*\exp@{\frac{-(x+y)z}{1-z}}\modBesselI{\alpha}@{\frac{2(xyz)^{\frac{1}{2}}}{1-z}}	${\displaystyle{\displaystyle|z|<1,\Re(\alpha+1)>0,\Re((\alpha)+k+1)>0}}$	sum((factorial(n)*LaguerreL(n, alpha, x)*LaguerreL(n, alpha, y))/(pochhammer(alpha + 1, n))*(x + y*I)^(n), n = 0..infinity) = (GAMMA(alpha + 1)*(x*y*(x + y*I))^(-(1)/(2)*alpha))/(1 -(x + y*I))* exp((-(x + y)*(x + y*I))/(1 -(x + y*I)))*BesselI(alpha, (2*(x*y*(x + y*I))^((1)/(2)))/(1 -(x + y*I)))	Sum[Divide[(n)!*LaguerreL[n, \[Alpha], x]*LaguerreL[n, \[Alpha], y],Pochhammer[\[Alpha]+ 1, n]]*(x + y*I)^(n), {n, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[\[Alpha]+ 1]*(x*y*(x + y*I))^(-Divide[1,2]*\[Alpha]),1 -(x + y*I)]* Exp[Divide[-(x + y)*(x + y*I),1 -(x + y*I)]]*BesselI[\[Alpha], Divide[2*(x*y*(x + y*I))^(Divide[1,2]),1 -(x + y*I)]]	Missing Macro Error	Failure	-	Failed [54 / 54] Result: Plus[Complex[-0.2554853305235294, -0.2809050421578725], NSum[Times[Power[Complex[1.5, -1.5], n], Factorial[n], LaguerreL[n, 1.5, -1.5], LaguerreL[n, 1.5, 1.5], Power[Pochhammer[2.5, n], -1]] Test Values: {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5]} Result: Plus[Complex[0.5256093118420817, -0.5266734460651719], NSum[Times[Power[Complex[1.5, -1.5], n], Factorial[n], LaguerreL[n, 0.5, -1.5], LaguerreL[n, 0.5, 1.5], Power[Pochhammer[1.5, n], -1]] Test Values: {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[x, 1.5], Rule[y, -1.5], Rule[α, 0.5]} ... skip entries to safe data
18.18.E28	${\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{H_{n}\left(x\right)H_{n}\left(y\right)}{2^{n}n!}z^{n}=(1-z^{2})^{-\frac{1}{2}}\exp\left(\frac{2xyz-(x^{2}+y^{2})z^{2}}{1-z^{2}}\right)}}$ \sum_{n=0}^{\infty}\frac{\HermitepolyH{n}@{x}\HermitepolyH{n}@{y}}{2^{n}n!}z^{n} = (1-z^{2})^{-\frac{1}{2}}\exp@{\frac{2xyz-(x^{2}+y^{2})z^{2}}{1-z^{2}}}	${\displaystyle{\displaystyle|z|<1}}$	sum((HermiteH(n, x)*HermiteH(n, y))/((2)^(n)* factorial(n))*(x + y*I)^(n), n = 0..infinity) = (1 -(x + y*I)^(2))^(-(1)/(2))* exp((2*x*y*(x + y*I)-((x)^(2)+ (y)^(2))*(x + y*I)^(2))/(1 -(x + y*I)^(2)))	Sum[Divide[HermiteH[n, x]*HermiteH[n, y],(2)^(n)* (n)!]*(x + y*I)^(n), {n, 0, Infinity}, GenerateConditions->None] == (1 -(x + y*I)^(2))^(-Divide[1,2])* Exp[Divide[2*x*y*(x + y*I)-((x)^(2)+ (y)^(2))*(x + y*I)^(2),1 -(x + y*I)^(2)]]	Failure	Failure	Manual Skip!	Failed [18 / 18] Result: Plus[Complex[45.14577089044274, -92.71442284704277], NSum[Times[Power[Complex[0.75, -0.75], n], Power[Factorial[n], -1], HermiteH[n, -1.5], HermiteH[n, 1.5]] Test Values: {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[x, 1.5], Rule[y, -1.5]} Result: Plus[Complex[-1.1210206126790663, -11.104063395584024], NSum[Times[Power[Complex[0.75, 0.75], n], Power[Factorial[n], -1], Power[HermiteH[n, 1.5], 2]] Test Values: {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
18.18.E29	${\displaystyle{\displaystyle\sum_{\ell=0}^{n}C^{(\lambda)}_{\ell}\left(x\right)C^{(\mu)}_{n-\ell}\left(x\right)=C^{(\lambda+\mu)}_{n}\left(x\right)}}$ \sum_{\ell=0}^{n}\ultrasphpoly{\lambda}{\ell}@{x}\ultrasphpoly{\mu}{n-\ell}@{x} = \ultrasphpoly{\lambda+\mu}{n}@{x}		sum(GegenbauerC(ell, lambda, x)*GegenbauerC(n - ell, mu, x), ell = 0..n) = GegenbauerC(n, lambda + mu, x)	Sum[GegenbauerC[\[ScriptL], \[Lambda], x]*GegenbauerC[n - \[ScriptL], \[Mu], x], {\[ScriptL], 0, n}, GenerateConditions->None] == GegenbauerC[n, \[Lambda]+ \[Mu], x]	Failure	Successful	Failed [36 / 300] Result: -3.000000000+0.*I Test Values: {lambda = 1/2*3^(1/2)+1/2*I, mu = -1/2*3^(1/2)-1/2*I, x = 3/2, n = 1} Result: -3.499999999+0.*I Test Values: {lambda = 1/2*3^(1/2)+1/2*I, mu = -1/2*3^(1/2)-1/2*I, x = 3/2, n = 2} ... skip entries to safe data	Successful [Tested: 300]
18.18.E30	${\displaystyle{\displaystyle\sum_{\ell=0}^{n}\frac{\ell+2\lambda}{2\lambda}C^{(\lambda)}_{\ell}\left(x\right)x^{n-\ell}=C^{(\lambda+1)}_{n}\left(x\right)}}$ \sum_{\ell=0}^{n}\frac{\ell+2\lambda}{2\lambda}\ultrasphpoly{\lambda}{\ell}@{x}x^{n-\ell} = \ultrasphpoly{\lambda+1}{n}@{x}		sum((ell + 2*lambda)/(2*lambda)*GegenbauerC(ell, lambda, x)*(x)^(n - ell), ell = 0..n) = GegenbauerC(n, lambda + 1, x)	Sum[Divide[\[ScriptL]+ 2*\[Lambda],2*\[Lambda]]*GegenbauerC[\[ScriptL], \[Lambda], x]*(x)^(n - \[ScriptL]), {\[ScriptL], 0, n}, GenerateConditions->None] == GegenbauerC[n, \[Lambda]+ 1, x]	Failure	Failure	Successful [Tested: 90]	Successful [Tested: 90]
18.18.E31	${\displaystyle{\displaystyle\sum_{\ell=0}^{n}T_{\ell}\left(x\right)x^{n-\ell}=U_{n}\left(x\right)}}$ \sum_{\ell=0}^{n}\ChebyshevpolyT{\ell}@{x}x^{n-\ell} = \ChebyshevpolyU{n}@{x}		sum(ChebyshevT(ell, x)*(x)^(n - ell), ell = 0..n) = ChebyshevU(n, x)	Sum[ChebyshevT[\[ScriptL], x]*(x)^(n - \[ScriptL]), {\[ScriptL], 0, n}, GenerateConditions->None] == ChebyshevU[n, x]	Failure	Aborted	Successful [Tested: 9]	Successful [Tested: 9]
18.18.E32	${\displaystyle{\displaystyle 2\sum_{\ell=0}^{n}T_{2\ell}\left(x\right)=1+U_{2n}\left(x\right)}}$ 2\sum_{\ell=0}^{n}\ChebyshevpolyT{2\ell}@{x} = 1+\ChebyshevpolyU{2n}@{x}		2*sum(ChebyshevT(2*ell, x), ell = 0..n) = 1 + ChebyshevU(2*n, x)	2*Sum[ChebyshevT[2*\[ScriptL], x], {\[ScriptL], 0, n}, GenerateConditions->None] == 1 + ChebyshevU[2*n, x]	Failure	Successful	Successful [Tested: 9]	Successful [Tested: 9]
18.18.E33	${\displaystyle{\displaystyle 2\sum_{\ell=0}^{n}T_{2\ell+1}\left(x\right)=U_{2n+1}\left(x\right)}}$ 2\sum_{\ell=0}^{n}\ChebyshevpolyT{2\ell+1}@{x} = \ChebyshevpolyU{2n+1}@{x}		2*sum(ChebyshevT(2*ell + 1, x), ell = 0..n) = ChebyshevU(2*n + 1, x)	2*Sum[ChebyshevT[2*\[ScriptL]+ 1, x], {\[ScriptL], 0, n}, GenerateConditions->None] == ChebyshevU[2*n + 1, x]	Failure	Successful	Successful [Tested: 9]	Successful [Tested: 9]
18.18.E34	${\displaystyle{\displaystyle 2(1-x^{2})\sum_{\ell=0}^{n}U_{2\ell}\left(x\right)=1-T_{2n+2}\left(x\right)}}$ 2(1-x^{2})\sum_{\ell=0}^{n}\ChebyshevpolyU{2\ell}@{x} = 1-\ChebyshevpolyT{2n+2}@{x}		2*(1 - (x)^(2))*sum(ChebyshevU(2*ell, x), ell = 0..n) = 1 - ChebyshevT(2*n + 2, x)	2*(1 - (x)^(2))*Sum[ChebyshevU[2*\[ScriptL], x], {\[ScriptL], 0, n}, GenerateConditions->None] == 1 - ChebyshevT[2*n + 2, x]	Failure	Successful	Successful [Tested: 9]	Successful [Tested: 9]
18.18.E35	${\displaystyle{\displaystyle 2(1-x^{2})\sum_{\ell=0}^{n}U_{2\ell+1}\left(x\right)=x-T_{2n+3}\left(x\right)}}$ 2(1-x^{2})\sum_{\ell=0}^{n}\ChebyshevpolyU{2\ell+1}@{x} = x-\ChebyshevpolyT{2n+3}@{x}		2*(1 - (x)^(2))*sum(ChebyshevU(2*ell + 1, x), ell = 0..n) = x - ChebyshevT(2*n + 3, x)	2*(1 - (x)^(2))*Sum[ChebyshevU[2*\[ScriptL]+ 1, x], {\[ScriptL], 0, n}, GenerateConditions->None] == x - ChebyshevT[2*n + 3, x]	Failure	Successful	Successful [Tested: 9]	Successful [Tested: 9]
18.18.E36	${\displaystyle{\displaystyle\sum_{\ell=0}^{n}P_{\ell}\left(x\right)P_{n-\ell}\left(x\right)=U_{n}\left(x\right)}}$ \sum_{\ell=0}^{n}\LegendrepolyP{\ell}@{x}\LegendrepolyP{n-\ell}@{x} = \ChebyshevpolyU{n}@{x}		sum(LegendreP(ell, x)*LegendreP(n - ell, x), ell = 0..n) = ChebyshevU(n, x)	Sum[LegendreP[\[ScriptL], x]*LegendreP[n - \[ScriptL], x], {\[ScriptL], 0, n}, GenerateConditions->None] == ChebyshevU[n, x]	Failure	Successful	Successful [Tested: 9]	Successful [Tested: 9]
18.18.E37	${\displaystyle{\displaystyle\sum_{\ell=0}^{n}L^{(\alpha)}_{\ell}\left(x\right)=L^{(\alpha+1)}_{n}\left(x\right)}}$ \sum_{\ell=0}^{n}\LaguerrepolyL[\alpha]{\ell}@{x} = \LaguerrepolyL[\alpha+1]{n}@{x}		sum(LaguerreL(ell, alpha, x), ell = 0..n) = LaguerreL(n, alpha + 1, x)	Sum[LaguerreL[\[ScriptL], \[Alpha], x], {\[ScriptL], 0, n}, GenerateConditions->None] == LaguerreL[n, \[Alpha]+ 1, x]	Missing Macro Error	Successful	-	Successful [Tested: 27]
18.18.E38	${\displaystyle{\displaystyle\sum_{\ell=0}^{n}L^{(\alpha)}_{\ell}\left(x\right)L^{(\beta)}_{n-\ell}\left(y\right)=L^{(\alpha+\beta+1)}_{n}\left(x+y\right)}}$ \sum_{\ell=0}^{n}\LaguerrepolyL[\alpha]{\ell}@{x}\LaguerrepolyL[\beta]{n-\ell}@{y} = \LaguerrepolyL[\alpha+\beta+1]{n}@{x+y}		sum(LaguerreL(ell, alpha, x)*LaguerreL(n - ell, beta, y), ell = 0..n) = LaguerreL(n, alpha + beta + 1, x + y)	Sum[LaguerreL[\[ScriptL], \[Alpha], x]*LaguerreL[n - \[ScriptL], \[Beta], y], {\[ScriptL], 0, n}, GenerateConditions->None] == LaguerreL[n, \[Alpha]+ \[Beta]+ 1, x + y]	Missing Macro Error	Successful	-	Successful [Tested: 300]
18.18.E39	${\displaystyle{\displaystyle\sum_{\ell=0}^{n}\genfrac{(}{)}{0.0pt}{}{n}{\ell}H_{\ell}\left(2^{\frac{1}{2}}x\right)H_{n-\ell}\left(2^{\frac{1}{2}}y\right)=2^{\frac{1}{2}n}H_{n}\left(x+y\right)}}$ \sum_{\ell=0}^{n}\binom{n}{\ell}\HermitepolyH{\ell}@{2^{\frac{1}{2}}x}\HermitepolyH{n-\ell}@{2^{\frac{1}{2}}y} = 2^{\frac{1}{2}n}\HermitepolyH{n}@{x+y}		sum(binomial(n,ell)*HermiteH(ell, (2)^((1)/(2))* x)*HermiteH(n - ell, (2)^((1)/(2))* y), ell = 0..n) = (2)^((1)/(2)*n)* HermiteH(n, x + y)	Sum[Binomial[n,\[ScriptL]]*HermiteH[\[ScriptL], (2)^(Divide[1,2])* x]*HermiteH[n - \[ScriptL], (2)^(Divide[1,2])* y], {\[ScriptL], 0, n}, GenerateConditions->None] == (2)^(Divide[1,2]*n)* HermiteH[n, x + y]	Failure	Successful	Successful [Tested: 54]	Successful [Tested: 54]
18.18.E40	${\displaystyle{\displaystyle\sum_{\ell=0}^{n}\genfrac{(}{)}{0.0pt}{}{n}{\ell}H_{2\ell}\left(x\right)H_{2n-2\ell}\left(y\right)=(-1)^{n}2^{2n}n!L_{n}\left(x^{2}+y^{2}\right)}}$ \sum_{\ell=0}^{n}\binom{n}{\ell}\HermitepolyH{2\ell}@{x}\HermitepolyH{2n-2\ell}@{y} = (-1)^{n}2^{2n}n!\LaguerrepolyL[]{n}@{x^{2}+y^{2}}		sum(binomial(n,ell)*HermiteH(2*ell, x)*HermiteH(2*n - 2*ell, y), ell = 0..n) = (- 1)^(n)* (2)^(2*n)* factorial(n)*LaguerreL(n, (x)^(2)+ (y)^(2))	Sum[Binomial[n,\[ScriptL]]*HermiteH[2*\[ScriptL], x]*HermiteH[2*n - 2*\[ScriptL], y], {\[ScriptL], 0, n}, GenerateConditions->None] == (- 1)^(n)* (2)^(2*n)* (n)!*LaguerreL[n, (x)^(2)+ (y)^(2)]	Failure	Successful	Successful [Tested: 54]	Successful [Tested: 54]
18.19.E1	${\displaystyle{\displaystyle p_{n}(x)=p_{n}\left(x;a,b,\overline{a},\overline{b}\right)}}$ p_{n}(x) = \contHahnpolyp{n}@{x}{a}{b}{\conj{a}}{\conj{b}}		Error	Subscript[p, n][x] == I^(n)*Divide[Pochhammer[a + Conjugate[a], n]*Pochhammer[a + Conjugate[b], n], (n)!] * HypergeometricPFQ[{-(n), n + 2*Re[a + b] - 1, a + I*(x)}, {a + Conjugate[a], a + Conjugate[b]}, 1]	Missing Macro Error	Missing Macro Error	-	-
18.19.E2	${\displaystyle{\displaystyle w(z;a,b,\overline{a},\overline{b})=\Gamma\left(a+iz\right)\Gamma\left(b+iz\right)\Gamma\left(\overline{a}-iz\right)\Gamma\left(\overline{b}-iz\right)}}$ w(z;a,b,\conj{a},\conj{b}) = \EulerGamma@{a+iz}\EulerGamma@{b+iz}\EulerGamma@{\conj{a}-iz}\EulerGamma@{\conj{b}-iz}		w(z ; a , b , conjugate(a), conjugate(b)) = GAMMA(a + I*z)*GAMMA(b + I*z)*GAMMA(conjugate(a)- I*z)*GAMMA(conjugate(b)- I*z)	w[z ; a , b , Conjugate[a], Conjugate[b]] == Gamma[a + I*z]*Gamma[b + I*z]*Gamma[Conjugate[a]- I*z]*Gamma[Conjugate[b]- I*z]	Translation Error	Translation Error	-	-
18.19.E3	${\displaystyle{\displaystyle w(x)=w(x;a,b,\overline{a},\overline{b})}}$ w(x) = w(x;a,b,\conj{a},\conj{b})		w(x) = w(x ; a , b , conjugate(a), conjugate(b))	w[x] == w[x ; a , b , Conjugate[a], Conjugate[b]]	Translation Error	Translation Error	-	-
18.19.E3	${\displaystyle{\displaystyle w(x;a,b,\overline{a},\overline{b})=|\Gamma\left(a+\mathrm{i}x\right)\Gamma\left(b+\mathrm{i}x\right)|^{2}}}$ w(x;a,b,\conj{a},\conj{b}) = |\EulerGamma@{a+\iunit x}\EulerGamma@{b+\iunit x}|^{2}	${\displaystyle{\displaystyle\Re(a+\mathrm{i}x)>0,\Re(b+\mathrm{i}x)>0}}$	w(x ; a , b , conjugate(a), conjugate(b)) = (abs(GAMMA(a + I*x)*GAMMA(b + I*x)))^(2)	w[x ; a , b , Conjugate[a], Conjugate[b]] == (Abs[Gamma[a + I*x]*Gamma[b + I*x]])^(2)	Translation Error	Translation Error	-	-
18.19.E5	${\displaystyle{\displaystyle k_{n}=\frac{{\left(n+2\Re\left(a+b\right)-1\right)_{n}}}{n!}}}$ k_{n} = \frac{\Pochhammersym{n+2\realpart@{a+b}-1}{n}}{n!}		k[n] = (pochhammer(n + 2*Re(a + b)- 1, n))/(factorial(n))	Subscript[k, n] == Divide[Pochhammer[n + 2*Re[a + b]- 1, n],(n)!]	Failure	Failure	Failed [298 / 300] Result: 6.866025404+.5000000000*I Test Values: {a = -3/2, b = -3/2, k[n] = 1/2*3^(1/2)+1/2*I, n = 1} Result: -9.133974596+.5000000000*I Test Values: {a = -3/2, b = -3/2, k[n] = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [298 / 300] Result: Complex[6.866025403784438, 0.49999999999999994] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[Subscript[k, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-9.13397459621556, 0.49999999999999994] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[Subscript[k, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.19.E7	${\displaystyle{\displaystyle w^{(\lambda)}(z;\phi)=\Gamma\left(\lambda+iz\right)\Gamma\left(\lambda-iz\right)e^{(2\phi-\pi)z}}}$ w^{(\lambda)}(z;\phi) = \EulerGamma@{\lambda+iz}\EulerGamma@{\lambda-iz}e^{(2\phi-\pi)z}	${\displaystyle{\displaystyle\Re(\lambda+\mathrm{i}z)>0,\Re(\lambda-\mathrm{i}z)>0}}$	(w(z ; phi))^(lambda) = GAMMA(lambda + I*z)*GAMMA(lambda - I*z)*exp((2*phi - Pi)*z)	(w[z ; \[Phi]])^(\[Lambda]) == Gamma[\[Lambda]+ I*z]*Gamma[\[Lambda]- I*z]*Exp[(2*\[Phi]- Pi)*z]	Translation Error	Translation Error	-	-
18.19.E8	${\displaystyle{\displaystyle w(x)=w^{(\lambda)}(x;\phi)}}$ w(x) = w^{(\lambda)}(x;\phi)	${\displaystyle{\displaystyle\lambda>0,0<\phi,\phi<\pi}}$	w(x) = (w(x ; phi))^(lambda)	w[x] == (w[x ; \[Phi]])^(\[Lambda])	Translation Error	Translation Error	-	-
18.19.E8	${\displaystyle{\displaystyle w^{(\lambda)}(x;\phi)=\left|\Gamma\left(\lambda+\mathrm{i}x\right)\right|^{2}e^{(2\phi-\pi)x}}}$ w^{(\lambda)}(x;\phi) = \left|\EulerGamma@{\lambda+\iunit x}\right|^{2}e^{(2\phi-\pi)x}	${\displaystyle{\displaystyle\lambda>0,0<\phi,\phi<\pi,\Re(\lambda+\mathrm{i}x)>0}}$	(w(x ; phi))^(lambda) = (abs(GAMMA(lambda + I*x)))^(2)* exp((2*phi - Pi)*x)	(w[x ; \[Phi]])^(\[Lambda]) == (Abs[Gamma[\[Lambda]+ I*x]])^(2)* Exp[(2*\[Phi]- Pi)*x]	Translation Error	Translation Error	-	-
18.19#Ex2	${\displaystyle{\displaystyle k_{n}=\frac{(2\sin\phi)^{n}}{n!}}}$ k_{n} = \frac{(2\sin@@{\phi})^{n}}{n!}		k[n] = ((2*sin(phi))^(n))/(factorial(n))	Subscript[k, n] == Divide[(2*Sin[\[Phi]])^(n),(n)!]	Failure	Failure	Failed [300 / 300] Result: -.8519352650-.1751929262*I Test Values: {phi = 1/2*3^(1/2)+1/2*I, k[n] = 1/2*3^(1/2)+1/2*I, n = 1} Result: -.3817262820-.6599548910*I Test Values: {phi = 1/2*3^(1/2)+1/2*I, k[n] = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.851935264815837, -0.17519292644574008] Test Values: {Rule[n, 1], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[k, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.3817262816831334, -0.6599548913509004] Test Values: {Rule[n, 2], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[k, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.20.E8	${\displaystyle{\displaystyle C_{n}\left(x;a\right)={{}_{2}F_{0}}\left({-n,-x\atop-};-a^{-1}\right)}}$ \CharlierpolyC{n}@{x}{a} = \genhyperF{2}{0}@@{-n,-x}{-}{-a^{-1}}		Error	HypergeometricPFQ[{-(n), -(x)}, {}, -Divide[1,a]] == HypergeometricPFQ[{- n , - x}, {-}, - (a)^(- 1)]	Missing Macro Error	Missing Macro Error	-	-
18.20.E9	${\displaystyle{\displaystyle p_{n}\left(x;a,b,\overline{a},\overline{b}\right)=\frac{{\mathrm{i}^{n}}{\left(a+\overline{a}\right)_{n}}{\left(a+\overline{b}\right)_{n}}}{n!}\*{{}_{3}F_{2}}\left({-n,n+2\Re\left(a+b\right)-1,a+\mathrm{i}x\atop a+\overline{a},a+\overline{b}};1\right)}}$ \contHahnpolyp{n}@{x}{a}{b}{\conj{a}}{\conj{b}} = \frac{\iunit^{n}\Pochhammersym{a+\conj{a}}{n}\Pochhammersym{a+\conj{b}}{n}}{n!}\*\genhyperF{3}{2}@@{-n,n+2\realpart@{a+b}-1,a+\iunit x}{a+\conj{a},a+\conj{b}}{1}		Error	I^(n)*Divide[Pochhammer[a + Conjugate[a], n]*Pochhammer[a + Conjugate[b], n], (n)!] * HypergeometricPFQ[{-(n), n + 2*Re[a + b] - 1, a + I*(x)}, {a + Conjugate[a], a + Conjugate[b]}, 1] == Divide[(I)^(n)* Pochhammer[a + Conjugate[a], n]*Pochhammer[a + Conjugate[b], n],(n)!]* HypergeometricPFQ[{- n , n + 2*Re[a + b]- 1 , a + I*x}, {a + Conjugate[a], a + Conjugate[b]}, 1]	Missing Macro Error	Missing Macro Error	-	-
18.21#Ex3	${\displaystyle{\displaystyle C_{n}\left(x;a\right)=C_{x}\left(n;a\right)}}$ \CharlierpolyC{n}@{x}{a} = \CharlierpolyC{x}@{n}{a}		Error	HypergeometricPFQ[{-(n), -(x)}, {}, -Divide[1,a]] == HypergeometricPFQ[{-(x), -(n)}, {}, -Divide[1,a]]	Missing Macro Error	Missing Macro Error	-	-
18.21.E9	${\displaystyle{\displaystyle\lim_{a\to\infty}(2a)^{\frac{1}{2}n}C_{n}\left((2a)^{\frac{1}{2}}x+a;a\right)=(-1)^{n}H_{n}\left(x\right)}}$ \lim_{a\to\infty}(2a)^{\frac{1}{2}n}\CharlierpolyC{n}@{(2a)^{\frac{1}{2}}x+a}{a} = (-1)^{n}\HermitepolyH{n}@{x}		Error	Limit[(2*a)^(Divide[1,2]*n)* HypergeometricPFQ[{-(n), -((2*a)^(Divide[1,2])* x + a)}, {}, -Divide[1,a]], a -> Infinity, GenerateConditions->None] == (- 1)^(n)* HermiteH[n, x]	Missing Macro Error	Missing Macro Error	-	-
18.22.E2	${\displaystyle{\displaystyle-xp_{n}(x)=A_{n}p_{n+1}(x)-\left(A_{n}+C_{n}\right)p_{n}(x)+C_{n}p_{n-1}(x)}}$ -xp_{n}(x) = A_{n}p_{n+1}(x)-\left(A_{n}+C_{n}\right)p_{n}(x)+C_{n}p_{n-1}(x)		- xp[n](x) = A[n]*p[n + 1](x)-(A[n]+((n*(n + alpha + beta + N + 1)*(n + beta))/((2*n + alpha + beta)*(2*n + alpha + beta + 1))))*p[n](x)+((n*(n + alpha + beta + N + 1)*(n + beta))/((2*n + alpha + beta)*(2*n + alpha + beta + 1)))*p[n - 1](x)	- Subscript[xp, n][x] == Subscript[A, n]*Subscript[p, n + 1][x]-(Subscript[A, n]+(Divide[n*(n + \[Alpha]+ \[Beta]+ N + 1)*(n + \[Beta]),(2*n + \[Alpha]+ \[Beta])*(2*n + \[Alpha]+ \[Beta]+ 1)]))*Subscript[p, n][x]+(Divide[n*(n + \[Alpha]+ \[Beta]+ N + 1)*(n + \[Beta]),(2*n + \[Alpha]+ \[Beta])*(2*n + \[Alpha]+ \[Beta]+ 1)])*Subscript[p, n - 1][x]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.22.E4	${\displaystyle{\displaystyle q_{n}(x)=\ifrac{p_{n}\left(x;a,b,\overline{a},\overline{b}\right)}{p_{n}\left(\mathrm{i}a;a,b,\overline{a},\overline{b}\right)}}}$ q_{n}(x) = \ifrac{\contHahnpolyp{n}@{x}{a}{b}{\conj{a}}{\conj{b}}}{\contHahnpolyp{n}@{\iunit a}{a}{b}{\conj{a}}{\conj{b}}}		Error	Subscript[q, n][x] == Divide[I^(n)*Divide[Pochhammer[a + Conjugate[a], n]*Pochhammer[a + Conjugate[b], n], (n)!] * HypergeometricPFQ[{-(n), n + 2*Re[a + b] - 1, a + I*(x)}, {a + Conjugate[a], a + Conjugate[b]}, 1],I^(n)*Divide[Pochhammer[a + Conjugate[a], n]*Pochhammer[a + Conjugate[b], n], (n)!] * HypergeometricPFQ[{-(n), n + 2*Re[a + b] - 1, a + I*(I*a)}, {a + Conjugate[a], a + Conjugate[b]}, 1]]	Missing Macro Error	Missing Macro Error	-	-
18.22.E8	${\displaystyle{\displaystyle(n+1)p_{n+1}(x)=2\left(x\sin\phi+(n+\lambda)\cos\phi\right)p_{n}(x)-(n+2\lambda-1)p_{n-1}(x)}}$ (n+1)p_{n+1}(x) = 2\left(x\sin@@{\phi}+(n+\lambda)\cos@@{\phi}\right)p_{n}(x)-(n+2\lambda-1)p_{n-1}(x)		(n + 1)*p[n + 1](x) = 2*(x*sin(phi)+(n + lambda)*cos(phi))*p[n](x)-(n + 2*lambda - 1)*p[n - 1](x)	(n + 1)*Subscript[p, n + 1][x] == 2*(x*Sin[\[Phi]]+(n + \[Lambda])*Cos[\[Phi]])*Subscript[p, n][x]-(n + 2*\[Lambda]- 1)*Subscript[p, n - 1][x]	Failure	Failure	Failed [300 / 300] Result: -3.110426782-.517373007*I Test Values: {lambda = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2, p[n] = 1/2*3^(1/2)+1/2*I, p[n-1] = 1/2*3^(1/2)+1/2*I, p[n+1] = 1/2*3^(1/2)+1/2*I, n = 1} Result: -3.005781337+.918117648*I Test Values: {lambda = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2, p[n] = 1/2*3^(1/2)+1/2*I, p[n-1] = 1/2*3^(1/2)+1/2*I, p[n+1] = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-3.110426781913132, -0.5173730098941742] Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, Plus[-1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-3.005781335086172, 0.9181176450774369] Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, Plus[-1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.22.E10	${\displaystyle{\displaystyle A(x)p_{n}(x+1)-\left(A(x)+C(x)\right)p_{n}(x)+C(x)p_{n}(x-1)-n(n+\alpha+\beta+1)p_{n}(x)=0}}$ A(x)p_{n}(x+1)-\left(A(x)+C(x)\right)p_{n}(x)+C(x)p_{n}(x-1)-n(n+\alpha+\beta+1)p_{n}(x) = 0		A(x)* p[n](x + 1)-(A(x)+(x*(x - beta - N - 1)))*p[n](x)+(x*(x - beta - N - 1))*p[n](x - 1)- n*(n + alpha + beta + 1)*p[n](x) = 0	A[x]* Subscript[p, n][x + 1]-(A[x]+(x*(x - \[Beta]- N - 1)))*Subscript[p, n][x]+(x*(x - \[Beta]- N - 1))*Subscript[p, n][x - 1]- n*(n + \[Alpha]+ \[Beta]+ 1)*Subscript[p, n][x] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
18.22.E12	${\displaystyle{\displaystyle A(x)p_{n}(x+1)-\left(A(x)+C(x)\right)p_{n}(x)+C(x)p_{n}(x-1)+\lambda_{n}p_{n}(x)=0}}$ A(x)p_{n}(x+1)-\left(A(x)+C(x)\right)p_{n}(x)+C(x)p_{n}(x-1)+\lambda_{n}p_{n}(x) = 0		A(x)* p[n](x + 1)-(A(x)+ C(x))*p[n](x)+ C(x)* p[n](x - 1)+ lambda[n]*p[n](x) = 0	A[x]* Subscript[p, n][x + 1]-(A[x]+ C[x])*Subscript[p, n][x]+ C[x]* Subscript[p, n][x - 1]+ Subscript[\[Lambda], n]*Subscript[p, n][x] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
18.22.E13	${\displaystyle{\displaystyle p_{n}(x)=p_{n}\left(x;a,b,\overline{a},\overline{b}\right)}}$ p_{n}(x) = \contHahnpolyp{n}@{x}{a}{b}{\conj{a}}{\conj{b}}		Error	Subscript[p, n][x] == I^(n)*Divide[Pochhammer[a + Conjugate[a], n]*Pochhammer[a + Conjugate[b], n], (n)!] * HypergeometricPFQ[{-(n), n + 2*Re[a + b] - 1, a + I*(x)}, {a + Conjugate[a], a + Conjugate[b]}, 1]	Missing Macro Error	Missing Macro Error	-	-
18.22.E14	${\displaystyle{\displaystyle A(x)p_{n}(x+i)-\left(A(x)+C(x)\right)p_{n}(x)+C(x)p_{n}(x-i)+n(n+2\Re\left(a+b\right)-1)p_{n}(x)=0}}$ A(x)p_{n}(x+i)-\left(A(x)+C(x)\right)p_{n}(x)+C(x)p_{n}(x-i)+n(n+2\realpart@{a+b}-1)p_{n}(x) = 0		A(x)* p[n](x + I)-(A(x)+((x - I*a)*(x - I*b)))*p[n](x)+((x - I*a)*(x - I*b))*p[n](x - I)+ n*(n + 2*Re(a + b)- 1)*p[n](x) = 0	A[x]* Subscript[p, n][x + I]-(A[x]+((x - I*a)*(x - I*b)))*Subscript[p, n][x]+((x - I*a)*(x - I*b))*Subscript[p, n][x - I]+ n*(n + 2*Re[a + b]- 1)*Subscript[p, n][x] == 0	Failure	Failure	Failed [300 / 300] Result: -5.196152425-1.499999999*I Test Values: {A = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, x = 3/2, p[n] = 1/2*3^(1/2)+1/2*I, n = 1} Result: -10.39230485-4.499999999*I Test Values: {A = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, x = 3/2, p[n] = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-5.196152422706632, -1.5] Test Values: {Rule[a, -1.5], Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[b, -1.5], Rule[n, 1], Rule[x, 1.5], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-10.392304845413264, -4.5] Test Values: {Rule[a, -1.5], Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[b, -1.5], Rule[n, 2], Rule[x, 1.5], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.22.E17	${\displaystyle{\displaystyle A(x)p_{n}(x+i)-\left(A(x)+C(x)\right)p_{n}(x)+C(x)p_{n}(x-i)+2n\sin\phi\,p_{n}(x)=0}}$ A(x)p_{n}(x+i)-\left(A(x)+C(x)\right)p_{n}(x)+C(x)p_{n}(x-i)+2n\sin@@{\phi}\,p_{n}(x) = 0		A(x)* p[n](x + I)-(A(x)+(exp(- I*phi)*(x - I*lambda)))*p[n](x)+(exp(- I*phi)*(x - I*lambda))*p[n](x - I)+ 2*n*sin(phi)*p[n](x) = 0	A[x]* Subscript[p, n][x + I]-(A[x]+(Exp[- I*\[Phi]]*(x - I*\[Lambda])))*Subscript[p, n][x]+(Exp[- I*\[Phi]]*(x - I*\[Lambda]))*Subscript[p, n][x - I]+ 2*n*Sin[\[Phi]]*Subscript[p, n][x] == 0	Failure	Failure	Failed [300 / 300] Result: -2.025869520+.288999556*I Test Values: {A = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2, p[n] = 1/2*3^(1/2)+1/2*I, n = 1} Result: -.300567841+2.454571398*I Test Values: {A = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2, p[n] = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-2.025869520811228, 0.28899955435496594] Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[x, 1.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.3005678430800254, 2.4545713959415254] Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[x, 1.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.23.E5	${\displaystyle{\displaystyle e^{z}\left(1-\frac{z}{a}\right)^{x}=\sum_{n=0}^{\infty}\frac{C_{n}\left(x;a\right)}{n!}z^{n}}}$ e^{z}\left(1-\frac{z}{a}\right)^{x} = \sum_{n=0}^{\infty}\frac{\CharlierpolyC{n}@{x}{a}}{n!}z^{n}		Error	Exp[x + y*I]*(1 -Divide[x + y*I,a])^(x) == Sum[Divide[HypergeometricPFQ[{-(n), -(x)}, {}, -Divide[1,a]],(n)!]*(x + y*I)^(n), {n, 0, Infinity}, GenerateConditions->None]	Missing Macro Error	Missing Macro Error	-	-
18.23.E6	${\displaystyle{\displaystyle{{}_{1}F_{1}}\left({a+\mathrm{i}x\atop 2\Re a};-\mathrm{i}z\right){{}_{1}F_{1}}\left({\overline{b}-\mathrm{i}x\atop 2\Re b};\mathrm{i}z\right)=\sum_{n=0}^{\infty}\frac{p_{n}\left(x;a,b,\overline{a},\overline{b}\right)}{{\left(2\Re a\right)_{n}}{\left(2\Re b\right)_{n}}}z^{n}}}$ \genhyperF{1}{1}@@{a+\iunit x}{2\realpart@@{a}}{-\iunit z}\genhyperF{1}{1}@@{\conj{b}-\iunit x}{2\realpart@@{b}}{\iunit z} = \sum_{n=0}^{\infty}\frac{\contHahnpolyp{n}@{x}{a}{b}{\conj{a}}{\conj{b}}}{\Pochhammersym{2\realpart@@{a}}{n}\Pochhammersym{2\realpart@@{b}}{n}}z^{n}		Error	HypergeometricPFQ[{a + I*x}, {2*Re[a]}, - I*(x + y*I)]*HypergeometricPFQ[{Conjugate[b]- I*x}, {2*Re[b]}, I*(x + y*I)] == Sum[Divide[I^(n)*Divide[Pochhammer[a + Conjugate[a], n]*Pochhammer[a + Conjugate[b], n], (n)!] * HypergeometricPFQ[{-(n), n + 2*Re[a + b] - 1, a + I*(x)}, {a + Conjugate[a], a + Conjugate[b]}, 1],Pochhammer[2*Re[a], n]*Pochhammer[2*Re[b], n]]*(x + y*I)^(n), {n, 0, Infinity}, GenerateConditions->None]	Missing Macro Error	Missing Macro Error	-	-
18.25#Ex1	${\displaystyle{\displaystyle-\delta-1<\beta}}$ -\delta-1 < \beta		- delta - 1 < beta	- \[Delta]- 1 < \[Beta]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.25#Ex2	${\displaystyle{\displaystyle N-1<-\delta-1}}$ N-1 < -\delta-1		N - 1 < - delta - 1	N - 1 < - \[Delta]- 1	Skipped - no semantic math	Skipped - no semantic math	-	-
18.25#Ex3	${\displaystyle{\displaystyle\gamma,\delta>-1,\quad\beta}}$ \gamma,\delta > -1,\quad\beta		gamma , delta > - 1	\[Gamma], \[Delta] > - 1	Skipped - no semantic math	Skipped - no semantic math	-	-
18.25#Ex4	${\displaystyle{\displaystyle\gamma,\delta>-1,\quad\beta}}$ \gamma,\delta > -1,\quad\beta		gamma , delta > - 1	\[Gamma], \[Delta] > - 1	Skipped - no semantic math	Skipped - no semantic math	-	-
18.25#Ex5	${\displaystyle{\displaystyle N-1<N+\gamma}}$ N-1 < N+\gamma		N - 1 < N + gamma	N - 1 < N + \[Gamma]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.25#Ex6	${\displaystyle{\displaystyle N+\gamma<\beta}}$ N+\gamma < \beta		N + gamma < beta	N + \[Gamma] < \[Beta]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.25#Ex7	${\displaystyle{\displaystyle\gamma,\delta<-N,\quad\beta}}$ \gamma,\delta < -N,\quad\beta		gamma , delta < - N	\[Gamma], \[Delta] < - N	Skipped - no semantic math	Skipped - no semantic math	-	-
18.25#Ex8	${\displaystyle{\displaystyle\gamma,\delta<-N,\quad\beta}}$ \gamma,\delta < -N,\quad\beta		gamma , delta < - N	\[Gamma], \[Delta] < - N	Skipped - no semantic math	Skipped - no semantic math	-	-
18.25.E4	${\displaystyle{\displaystyle w(y^{2})=\frac{1}{2y}\left|\frac{\prod_{j}\Gamma\left(a_{j}+iy\right)}{\Gamma\left(2iy\right)}\right|^{2}}}$ w(y^{2}) = \frac{1}{2y}\left|\frac{\prod_{j}\EulerGamma@{a_{j}+iy}}{\EulerGamma@{2iy}}\right|^{2}		w((y)^(2)) = (1)/(2*y)*(abs((product(GAMMA(a[j]+ I*y), j = - infinity..infinity))/(GAMMA(2*I*y))))^(2)	w[(y)^(2)] == Divide[1,2*y]*(Abs[Divide[Product[Gamma[Subscript[a, j]+ I*y], {j, - Infinity, Infinity}, GenerateConditions->None],Gamma[2*I*y]]])^(2)	Failure	Failure	Error	Skip - No test values generated
18.25.E7	${\displaystyle{\displaystyle w(y^{2})=\frac{1}{2y}\left|\frac{\prod_{j}\Gamma\left(a_{j}+iy\right)}{\Gamma\left(2iy\right)}\right|^{2}}}$ w(y^{2}) = \frac{1}{2y}\left|\frac{\prod_{j}\EulerGamma@{a_{j}+iy}}{\EulerGamma@{2iy}}\right|^{2}		w((y)^(2)) = (1)/(2*y)*(abs((product(GAMMA(a[j]+ I*y), j = - infinity..infinity))/(GAMMA(2*I*y))))^(2)	w[(y)^(2)] == Divide[1,2*y]*(Abs[Divide[Product[Gamma[Subscript[a, j]+ I*y], {j, - Infinity, Infinity}, GenerateConditions->None],Gamma[2*I*y]]])^(2)	Failure	Failure	Error	Skip - No test values generated
18.25.E11	${\displaystyle{\displaystyle\omega_{y}=\frac{{\left(\alpha+1\right)_{y}}{\left(\beta+\delta+1\right)_{y}}{\left(\gamma+1\right)_{y}}{\left(\gamma+\delta+2\right)_{y}}}{{\left(-\alpha+\gamma+\delta+1\right)_{y}}{\left(-\beta+\gamma+1\right)_{y}}{\left(\delta+1\right)_{y}}y!}}}$ \omega_{y} = \frac{\Pochhammersym{\alpha+1}{y}\Pochhammersym{\beta+\delta+1}{y}\Pochhammersym{\gamma+1}{y}\Pochhammersym{\gamma+\delta+2}{y}}{\Pochhammersym{-\alpha+\gamma+\delta+1}{y}\Pochhammersym{-\beta+\gamma+1}{y}\Pochhammersym{\delta+1}{y}y!}		omega[y] = (pochhammer(alpha + 1, y)*pochhammer(beta + delta + 1, y)*pochhammer(gamma + 1, y)*pochhammer(gamma + delta + 2, y))/(pochhammer(- alpha + gamma + delta + 1, y)*pochhammer(- beta + gamma + 1, y)*pochhammer(delta + 1, y)*factorial(y))	Subscript[\[Omega], y] == Divide[Pochhammer[\[Alpha]+ 1, y]*Pochhammer[\[Beta]+ \[Delta]+ 1, y]*Pochhammer[\[Gamma]+ 1, y]*Pochhammer[\[Gamma]+ \[Delta]+ 2, y],Pochhammer[- \[Alpha]+ \[Gamma]+ \[Delta]+ 1, y]*Pochhammer[- \[Beta]+ \[Gamma]+ 1, y]*Pochhammer[\[Delta]+ 1, y]*(y)!]	Failure	Failure	Failed [300 / 300] Result: .3776605936+.3684973106*I Test Values: {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, y = -3/2, omega[y] = 1/2*3^(1/2)+1/2*I} Result: -.9883648104+.7345227146*I Test Values: {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, y = -3/2, omega[y] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Skipped - Because timed out
18.25.E14	${\displaystyle{\displaystyle\omega_{y}=\frac{(-1)^{y}{\left(-N\right)_{y}}{\left(\gamma+1\right)_{y}}{\left(\gamma+\delta+1\right)_{2}}}{{\left(N+\gamma+\delta+2\right)_{y}}{\left(\delta+1\right)_{y}}y!}}}$ \omega_{y} = \frac{(-1)^{y}\Pochhammersym{-N}{y}\Pochhammersym{\gamma+1}{y}\Pochhammersym{\gamma+\delta+1}{2}}{\Pochhammersym{N+\gamma+\delta+2}{y}\Pochhammersym{\delta+1}{y}y!}		omega[y] = ((- 1)^(y)* pochhammer(- N, y)*pochhammer(gamma + 1, y)*pochhammer(gamma + delta + 1, 2))/(pochhammer(N + gamma + delta + 2, y)*pochhammer(delta + 1, y)*factorial(y))	Subscript[\[Omega], y] == Divide[(- 1)^(y)* Pochhammer[- N, y]*Pochhammer[\[Gamma]+ 1, y]*Pochhammer[\[Gamma]+ \[Delta]+ 1, 2],Pochhammer[N + \[Gamma]+ \[Delta]+ 2, y]*Pochhammer[\[Delta]+ 1, y]*(y)!]	Failure	Failure	Failed [300 / 300] Result: -3.383353139+40.73029447*I Test Values: {N = 1/2*3^(1/2)+1/2*I, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, y = -3/2, omega[y] = 1/2*3^(1/2)+1/2*I} Result: -4.749378543+41.09631987*I Test Values: {N = 1/2*3^(1/2)+1/2*I, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, y = -3/2, omega[y] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[4.68201860981384, 5.925892618408873] Test Values: {Rule[N, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[3.3159932060294013, 6.291918022193311] Test Values: {Rule[N, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, y], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
18.27.E1	${\displaystyle{\displaystyle A(x)p_{n}(qx)+B(x)p_{n}(x)+C(x)p_{n}(q^{-1}x)=\lambda_{n}p_{n}(x)}}$ A(x)p_{n}(qx)+B(x)p_{n}(x)+C(x)p_{n}(q^{-1}x) = \lambda_{n}p_{n}(x)		A(x)* p[n](q*x)+ B(x)* p[n](x)+ C(x)* p[n]((q)^(- 1)* x) = lambda[n]*p[n](x)	A[x]* Subscript[p, n][q*x]+ B[x]* Subscript[p, n][x]+ C[x]* Subscript[p, n][(q)^(- 1)* x] == Subscript[\[Lambda], n]*Subscript[p, n][x]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.27.E9	${\displaystyle{\displaystyle v_{x}=\frac{(a^{-1}x,c^{-1}x;q)_{\infty}}{(x,bc^{-1}x;q)_{\infty}}}}$ v_{x} = \frac{(a^{-1}x,c^{-1}x;q)_{\infty}}{(x,bc^{-1}x;q)_{\infty}}	${\displaystyle{\displaystyle 0<a,a<q^{-1},0<b,b<q^{-1},c<0}}$	v[x] = ((a)^(- 1)* x , (c)^(- 1)* x ; q[infinity])/(x , b*(c)^(- 1)* x ; q[infinity])	Subscript[v, x] == Divide[Subscript[(a)^(- 1)* x , (c)^(- 1)* x ; q, Infinity],Subscript[x , b*(c)^(- 1)* x ; q, Infinity]]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.27.E12	${\displaystyle{\displaystyle v_{x}=\frac{(qx/c,-qx/d;q)_{\infty}}{(q^{\alpha+1}x/c,-q^{\beta+1}x/d;q)_{\infty}}}}$ v_{x} = \frac{(qx/c,-qx/d;q)_{\infty}}{(q^{\alpha+1}x/c,-q^{\beta+1}x/d;q)_{\infty}}	${\displaystyle{\displaystyle\alpha>-1,\beta>-1,c>0,d>0}}$	v[x] = (q*x/c , - q*x/d ; q[infinity])/((q)^(alpha + 1)* x/c , - (q)^(beta + 1)* x/d ; q[infinity])	Subscript[v, x] == Divide[Subscript[q*x/c , - q*x/d ; q, Infinity],Subscript[(q)^(\[Alpha]+ 1)* x/c , - (q)^(\[Beta]+ 1)* x/d ; q, Infinity]]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.27.E21	${\displaystyle{\displaystyle\left(q;q\right)_{n}\sum_{\ell=0}^{\left\lfloor n/2\right\rfloor}\frac{(-1)^{\ell}q^{\ell(\ell-1)}x^{n-2\ell}}{\left(q^{2};q^{2}\right)_{\ell}\left(q;q\right)_{n-2\ell}}=x^{n}{{}_{2}\phi_{0}}\left({q^{-n},q^{-n+1}\atop-};q^{2},x^{-2}q^{2n-1}\right)}}$ \qPochhammer{q}{q}{n}\sum_{\ell=0}^{\floor{n/2}}\frac{(-1)^{\ell}q^{\ell(\ell-1)}x^{n-2\ell}}{\qPochhammer{q^{2}}{q^{2}}{\ell}\qPochhammer{q}{q}{n-2\ell}} = x^{n}\qgenhyperphi{2}{0}@@{q^{-n},q^{-n+1}}{-}{q^{2}}{x^{-2}q^{2n-1}}		Error	QPochhammer[q, q, n]*Sum[Divide[(- 1)^\[ScriptL]* (q)^(\[ScriptL]*(\[ScriptL]- 1))* (x)^(n - 2*\[ScriptL]),QPochhammer[(q)^(2), (q)^(2), \[ScriptL]]*QPochhammer[q, q, n - 2*\[ScriptL]]], {\[ScriptL], 0, Floor[n/2]}, GenerateConditions->None] == (x)^(n)* QHypergeometricPFQ[{(q)^(- n), (q)^(- n + 1)},{-},(q)^(2),(x)^(- 2)* (q)^(2*n - 1)]	Missing Macro Error	Failure	-	Error
18.27.E23	${\displaystyle{\displaystyle\left(q;q\right)_{n}\sum_{\ell=0}^{\left\lfloor n/2\right\rfloor}\frac{(-1)^{\ell}q^{-2n\ell}q^{\ell(2\ell+1)}x^{n-2\ell}}{\left(q^{2};q^{2}\right)_{\ell}\left(q;q\right)_{n-2\ell}}=x^{n}{{}_{2}\phi_{1}}\left({q^{-n},q^{-n+1}\atop 0};q^{2},-x^{-2}q^{2}\right)}}$ \qPochhammer{q}{q}{n}\sum_{\ell=0}^{\floor{n/2}}\frac{(-1)^{\ell}q^{-2n\ell}q^{\ell(2\ell+1)}x^{n-2\ell}}{\qPochhammer{q^{2}}{q^{2}}{\ell}\qPochhammer{q}{q}{n-2\ell}} = x^{n}\qgenhyperphi{2}{1}@@{q^{-n},q^{-n+1}}{0}{q^{2}}{-x^{-2}q^{2}}		Error	QPochhammer[q, q, n]*Sum[Divide[(- 1)^\[ScriptL]* (q)^(- 2*n*\[ScriptL])* (q)^(\[ScriptL]*(2*\[ScriptL]+ 1))* (x)^(n - 2*\[ScriptL]),QPochhammer[(q)^(2), (q)^(2), \[ScriptL]]*QPochhammer[q, q, n - 2*\[ScriptL]]], {\[ScriptL], 0, Floor[n/2]}, GenerateConditions->None] == (x)^(n)* QHypergeometricPFQ[{(q)^(- n), (q)^(- n + 1)},{0},(q)^(2),- (x)^(- 2)* (q)^(2)]	Missing Macro Error	Aborted	-	Skipped - Because timed out
18.28.E1	${\displaystyle{\displaystyle a^{-n}\sum_{\ell=0}^{n}q^{\ell}\left(abq^{\ell},acq^{\ell},adq^{\ell};q\right)_{n-\ell}\*\frac{\left(q^{-n},abcdq^{n-1};q\right)_{\ell}}{\left(q;q\right)_{\ell}}\prod_{j=0}^{\ell-1}{(1-2aq^{j}\cos\theta+a^{2}q^{2j})}=a^{-n}\left(ab,ac,ad;q\right)_{n}\*{{}_{4}\phi_{3}}\left({q^{-n},abcdq^{n-1},ae^{\mathrm{i}\theta},ae^{-\mathrm{i}\theta}\atop ab,ac,ad};q,q\right)}}$ a^{-n}\sum_{\ell=0}^{n}q^{\ell}\qmultiPochhammersym{abq^{\ell},acq^{\ell},adq^{\ell}}{q}{n-\ell}\*\frac{\qmultiPochhammersym{q^{-n},abcdq^{n-1}}{q}{\ell}}{\qPochhammer{q}{q}{\ell}}\prod_{j=0}^{\ell-1}{(1-2aq^{j}\cos@@{\theta}+a^{2}q^{2j})} = a^{-n}\qmultiPochhammersym{ab,ac,ad}{q}{n}\*\qgenhyperphi{4}{3}@@{q^{-n},abcdq^{n-1},ae^{\iunit\theta},ae^{-\iunit\theta}}{ab,ac,ad}{q}{q}		Error	(a)^(- n)* Sum[(q)^\[ScriptL]* Product[QPochhammer[Part[{a*b*(q)^\[ScriptL], a*c*(q)^\[ScriptL], a*d*(q)^\[ScriptL]},i],q,n - \[ScriptL]],{i,1,Length[{a*b*(q)^\[ScriptL], a*c*(q)^\[ScriptL], a*d*(q)^\[ScriptL]}]}]*Divide[Product[QPochhammer[Part[{(q)^(- n), a*b*c*d*(q)^(n - 1)},i],q,\[ScriptL]],{i,1,Length[{(q)^(- n), a*b*c*d*(q)^(n - 1)}]}],QPochhammer[q, q, \[ScriptL]]]*Product[1 - 2*a*(q)^(j)* Cos[\[Theta]]+ (a)^(2)* (q)^(2*j), {j, 0, \[ScriptL]- 1}, GenerateConditions->None], {\[ScriptL], 0, n}, GenerateConditions->None] == (a)^(- n)* Product[QPochhammer[Part[{a*b , a*c , a*d},i],q,n],{i,1,Length[{a*b , a*c , a*d}]}]* QHypergeometricPFQ[{(q)^(- n), a*b*c*d*(q)^(n - 1), a*Exp[I*\[Theta]], a*Exp[- I*\[Theta]]},{a*b , a*c , a*d},q,q]	Missing Macro Error	Aborted	-	Skipped - Because timed out
18.28.E3	${\displaystyle{\displaystyle 2\pi\sin\theta\,w(\cos\theta)={\left|\frac{\left(e^{2i\theta};q\right)_{\infty}}{\left(ae^{i\theta},be^{i\theta},ce^{i\theta},de^{i\theta};q\right)_{\infty}}\right|^{2}}}}$ 2\pi\sin@@{\theta}\,w(\cos@@{\theta}) = \abs{\frac{\qPochhammer{e^{2i\theta}}{q}{\infty}}{\qmultiPochhammersym{ae^{i\theta},be^{i\theta},ce^{i\theta},de^{i\theta}}{q}{\infty}}}^{2}		Error	2*Pi*Sin[\[Theta]]*w[Cos[\[Theta]]] == (Abs[Divide[QPochhammer[Exp[2*I*\[Theta]], q, Infinity],Product[QPochhammer[Part[{a*Exp[I*\[Theta]], b*Exp[I*\[Theta]], c*Exp[I*\[Theta]], d*Exp[I*\[Theta]]},i],q,Infinity],{i,1,Length[{a*Exp[I*\[Theta]], b*Exp[I*\[Theta]], c*Exp[I*\[Theta]], d*Exp[I*\[Theta]]}]}]]])^(2)	Missing Macro Error	Failure	-	Skipped - Because timed out
18.28.E4	${\displaystyle{\displaystyle h_{0}=\frac{\left(abcd;q\right)_{\infty}}{\left(q,ab,ac,ad,bc,bd,cd;q\right)_{\infty}}}}$ h_{0} = \frac{\qPochhammer{abcd}{q}{\infty}}{\qmultiPochhammersym{q,ab,ac,ad,bc,bd,cd}{q}{\infty}}		Error	Subscript[h, 0] == Divide[QPochhammer[a*b*c*d, q, Infinity],Product[QPochhammer[Part[{q , a*b , a*c , a*d , b*c , b*d , c*d},i],q,Infinity],{i,1,Length[{q , a*b , a*c , a*d , b*c , b*d , c*d}]}]]	Missing Macro Error	Translation Error	-	-
18.28.E7	${\displaystyle{\displaystyle a^{-n}\sum_{\ell=0}^{n}q^{\ell}\frac{\left(abq^{\ell};q\right)_{n-\ell}\left(q^{-n};q\right)_{\ell}}{\left(q;q\right)_{\ell}}\*\prod_{j=0}^{\ell-1}(1-2aq^{j}\cos\theta+a^{2}q^{2j})=\frac{\left(ab;q\right)_{n}}{a^{n}}{{}_{3}\phi_{2}}\left({q^{-n},ae^{\mathrm{i}\theta},ae^{-\mathrm{i}\theta}\atop ab,0};q,q\right)}}$ a^{-n}\sum_{\ell=0}^{n}q^{\ell}\frac{\qPochhammer{abq^{\ell}}{q}{n-\ell}\qPochhammer{q^{-n}}{q}{\ell}}{\qPochhammer{q}{q}{\ell}}\*\prod_{j=0}^{\ell-1}(1-2aq^{j}\cos@@{\theta}+a^{2}q^{2j}) = \frac{\qPochhammer{ab}{q}{n}}{a^{n}}\qgenhyperphi{3}{2}@@{q^{-n},ae^{\iunit\theta},ae^{-\iunit\theta}}{ab,0}{q}{q}		Error	(a)^(- n)* Sum[(q)^\[ScriptL]*Divide[QPochhammer[a*b*(q)^\[ScriptL], q, n - \[ScriptL]]*QPochhammer[(q)^(- n), q, \[ScriptL]],QPochhammer[q, q, \[ScriptL]]]* Product[1 - 2*a*(q)^(j)* Cos[\[Theta]]+ (a)^(2)* (q)^(2*j), {j, 0, \[ScriptL]- 1}, GenerateConditions->None], {\[ScriptL], 0, n}, GenerateConditions->None] == Divide[QPochhammer[a*b, q, n],(a)^(n)]*QHypergeometricPFQ[{(q)^(- n), a*Exp[I*\[Theta]], a*Exp[- I*\[Theta]]},{a*b , 0},q,q]	Missing Macro Error	Aborted	-	Skipped - Because timed out
18.28.E7	${\displaystyle{\displaystyle\frac{\left(ab;q\right)_{n}}{a^{n}}{{}_{3}\phi_{2}}\left({q^{-n},ae^{\mathrm{i}\theta},ae^{-\mathrm{i}\theta}\atop ab,0};q,q\right)=\left(be^{-\mathrm{i}\theta};q\right)_{n}e^{\mathrm{i}n\theta}{{}_{2}\phi_{1}}\left({q^{-n},ae^{\mathrm{i}\theta}\atop b^{-1}q^{1-n}e^{\mathrm{i}\theta}};q,b^{-1}qe^{-\mathrm{i}\theta}\right)}}$ \frac{\qPochhammer{ab}{q}{n}}{a^{n}}\qgenhyperphi{3}{2}@@{q^{-n},ae^{\iunit\theta},ae^{-\iunit\theta}}{ab,0}{q}{q} = \qPochhammer{be^{-\iunit\theta}}{q}{n}e^{\iunit n\theta}\qgenhyperphi{2}{1}@@{q^{-n},ae^{\iunit\theta}}{b^{-1}q^{1-n}e^{\iunit\theta}}{q}{b^{-1}qe^{-\iunit\theta}}		Error	Divide[QPochhammer[a*b, q, n],(a)^(n)]*QHypergeometricPFQ[{(q)^(- n), a*Exp[I*\[Theta]], a*Exp[- I*\[Theta]]},{a*b , 0},q,q] == QPochhammer[b*Exp[- I*\[Theta]], q, n]*Exp[I*n*\[Theta]]*QHypergeometricPFQ[{(q)^(- n), a*Exp[I*\[Theta]]},{(b)^(- 1)* (q)^(1 - n)* Exp[I*\[Theta]]},q,(b)^(- 1)* q*Exp[- I*\[Theta]]]	Missing Macro Error	Failure	-	Failed [240 / 300] Result: Plus[Times[Complex[-1.8929465558343552, -0.4620307840711053], QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], Complex[-0.5894198337515327, -0.693046176106658]} Test Values: {Complex[-0.2619643705562368, -0.3080205227140702]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-1.0353339124695373, 0.3690649628228472]]], Times[0.8333333333333333, QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], Complex[-0.5894198337515327, -0.693046176106658], Complex[-1.6022092234201426, 1.8838948267937556]}, {2.25, 0.0}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Plus[Times[Complex[-2.642841004049141, -3.076058498066829], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], Complex[-0.5894198337515327, -0.693046176106658]} Test Values: {Complex[-0.38087806114513634, -0.13577141227922815]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-1.0353339124695373, 0.3690649628228472]]], Times[Complex[0.5269761991749927, 0.6249999999999999], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], Complex[-0.5894198337515327, -0.693046176106658], Complex[-1.6022092234201426, 1.8838948267937556]}, {2.25, 0.0}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.28.E11	${\displaystyle{\displaystyle 0<q}}$ 0 < q		0 < q	0 < q	Failure	Failure	Failed [3 / 10] Result: 0. < -1.500000000 Test Values: {q = -3/2} Result: 0. < -.5000000000 Test Values: {q = -1/2} ... skip entries to safe data	Failed [7 / 10] Result: Less[0.0, Complex[0.8660254037844387, 0.49999999999999994]] Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Less[0.0, Complex[-0.4999999999999998, 0.8660254037844387]] Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
18.28.E11	${\displaystyle{\displaystyle q<1,a,b\in\mathbb{R},ab}}$ q < 1,a,b\in\Reals,ab		q < 1; a , b in real , a*b	q < 1 a , b \[Element]Reals , a*b	Failure	Failure	Error	Error
18.28.E11	${\displaystyle{\displaystyle 1,a,b\in\mathbb{R},ab>1,a^{-1}b}}$ 1,a,b\in\Reals,ab > 1,a^{-1}b		1 , a , b in real; a*b > 1 , (a)^(- 1)* b	1 , a , b \[Element]Reals a*b > 1 , (a)^(- 1)* b	Error	Failure	Skip - symbolical successful subtest	Error
18.28.E11	${\displaystyle{\displaystyle 1,a^{-1}b<q^{-1}}}$ 1,a^{-1}b < q^{-1}		1 , (a)^(- 1)* b < (q)^(- 1)	1 , (a)^(- 1)* b < (q)^(- 1)	Failure	Failure	Error	Error
18.28.E12	${\displaystyle{\displaystyle 0<q}}$ 0 < q		0 < q	0 < q	Failure	Failure	Failed [3 / 10] Result: 0. < -1.500000000 Test Values: {q = -3/2} Result: 0. < -.5000000000 Test Values: {q = -1/2} ... skip entries to safe data	Failed [7 / 10] Result: Less[0.0, Complex[0.8660254037844387, 0.49999999999999994]] Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Less[0.0, Complex[-0.4999999999999998, 0.8660254037844387]] Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
18.28.E12	${\displaystyle{\displaystyle q<1,\ifrac{a}{\mathrm{i}},\ifrac{b}{\mathrm{i}}\in\mathbb{R},(\Im a)(\Im b)}}$ q < 1,\ifrac{a}{\iunit},\ifrac{b}{\iunit}\in\Reals,(\imagpart@@{a})(\imagpart@@{b})		q < 1; (a)/(I),(b)/(I) in real ,Im(a)*Im(b)	q < 1 Divide[a,I],Divide[b,I] \[Element]Reals ,Im[a]*Im[b]	Failure	Failure	Error	Error
18.28.E12	${\displaystyle{\displaystyle 1,\ifrac{a}{\mathrm{i}},\ifrac{b}{\mathrm{i}}\in\mathbb{R},(\Im a)(\Im b)>0,a^{-1}b}}$ 1,\ifrac{a}{\iunit},\ifrac{b}{\iunit}\in\Reals,(\imagpart@@{a})(\imagpart@@{b}) > 0,a^{-1}b		1 ,(a)/(I),(b)/(I) in real; Im(a)*Im(b) > 0 , (a)^(- 1)* b	1 ,Divide[a,I],Divide[b,I] \[Element]Reals Im[a]*Im[b] > 0 , (a)^(- 1)* b	Error	Failure	Skip - symbolical successful subtest	Error
18.28.E12	${\displaystyle{\displaystyle 0,a^{-1}b<q^{-1}}}$ 0,a^{-1}b < q^{-1}		0 , (a)^(- 1)* b < (q)^(- 1)	0 , (a)^(- 1)* b < (q)^(- 1)	Failure	Failure	Error	Error
18.28.E13	${\displaystyle{\displaystyle\sum_{\ell=0}^{n}\frac{\left(\beta;q\right)_{\ell}\left(\beta;q\right)_{n-\ell}}{\left(q;q\right)_{\ell}\left(q;q\right)_{n-\ell}}e^{\mathrm{i}(n-2\ell)\theta}=\frac{\left(\beta;q\right)_{n}}{\left(q;q\right)_{n}}e^{\mathrm{i}n\theta}{{}_{2}\phi_{1}}\left({q^{-n},\beta\atop\beta^{-1}q^{1-n}};q,\beta^{-1}qe^{-2\mathrm{i}\theta}\right)}}$ \sum_{\ell=0}^{n}\frac{\qPochhammer{\beta}{q}{\ell}\qPochhammer{\beta}{q}{n-\ell}}{\qPochhammer{q}{q}{\ell}\qPochhammer{q}{q}{n-\ell}}e^{\iunit(n-2\ell)\theta} = \frac{\qPochhammer{\beta}{q}{n}}{\qPochhammer{q}{q}{n}}e^{\iunit n\theta}\qgenhyperphi{2}{1}@@{q^{-n},\beta}{\beta^{-1}q^{1-n}}{q}{\beta^{-1}qe^{-2\iunit\theta}}		Error	Sum[Divide[QPochhammer[\[Beta], q, \[ScriptL]]*QPochhammer[\[Beta], q, n - \[ScriptL]],QPochhammer[q, q, \[ScriptL]]*QPochhammer[q, q, n - \[ScriptL]]]*Exp[I*(n - 2*\[ScriptL])*\[Theta]], {\[ScriptL], 0, n}, GenerateConditions->None] == Divide[QPochhammer[\[Beta], q, n],QPochhammer[q, q, n]]*Exp[I*n*\[Theta]]*QHypergeometricPFQ[{(q)^(- n), \[Beta]},{\[Beta]^(- 1)* (q)^(1 - n)},q,\[Beta]^(- 1)* q*Exp[- 2*I*\[Theta]]]	Missing Macro Error	Aborted	-	Skipped - Because timed out
18.28.E16	${\displaystyle{\displaystyle\sum_{\ell=0}^{n}\frac{\left(q;q\right)_{n}e^{\mathrm{i}(n-2\ell)\theta}}{\left(q;q\right)_{\ell}\left(q;q\right)_{n-\ell}}=e^{\mathrm{i}n\theta}{{}_{2}\phi_{0}}\left({q^{-n},0\atop-};q,q^{n}e^{-2\mathrm{i}\theta}\right)}}$ \sum_{\ell=0}^{n}\frac{\qPochhammer{q}{q}{n}e^{\iunit(n-2\ell)\theta}}{\qPochhammer{q}{q}{\ell}\qPochhammer{q}{q}{n-\ell}} = e^{\iunit n\theta}\qgenhyperphi{2}{0}@@{q^{-n},0}{-}{q}{q^{n}e^{-2\iunit\theta}}		Error	Sum[Divide[QPochhammer[q, q, n]*Exp[I*(n - 2*\[ScriptL])*\[Theta]],QPochhammer[q, q, \[ScriptL]]*QPochhammer[q, q, n - \[ScriptL]]], {\[ScriptL], 0, n}, GenerateConditions->None] == Exp[I*n*\[Theta]]*QHypergeometricPFQ[{(q)^(- n), 0},{-},q,(q)^(n)* Exp[- 2*I*\[Theta]]]	Missing Macro Error	Failure	-	Error
18.28.E18	${\displaystyle{\displaystyle\sum_{\ell=0}^{n}q^{\frac{1}{2}\ell(\ell+1)}\frac{\left(q^{-n};q\right)_{\ell}}{\left(q;q\right)_{\ell}}e^{(n-2\ell)t}=e^{nt}{{}_{1}\phi_{1}}\left({q^{-n}\atop 0};q,-qe^{-2t}\right)}}$ \sum_{\ell=0}^{n}q^{\frac{1}{2}\ell(\ell+1)}\frac{\qPochhammer{q^{-n}}{q}{\ell}}{\qPochhammer{q}{q}{\ell}}e^{(n-2\ell)t} = e^{nt}\qgenhyperphi{1}{1}@@{q^{-n}}{0}{q}{-qe^{-2t}}		Error	Sum[(q)^(Divide[1,2]*\[ScriptL]*(\[ScriptL]+ 1))*Divide[QPochhammer[(q)^(- n), q, \[ScriptL]],QPochhammer[q, q, \[ScriptL]]]*Exp[(n - 2*\[ScriptL])*t], {\[ScriptL], 0, n}, GenerateConditions->None] == Exp[n*t]*QHypergeometricPFQ[{(q)^(- n)},{0},q,- q*Exp[- 2*t]]	Missing Macro Error	Aborted	-	Skipped - Because timed out
18.30.E1	${\displaystyle{\displaystyle A_{n}A_{n+1}C_{n+1}>0}}$ A_{n}A_{n+1}C_{n+1} > 0	${\displaystyle{\displaystyle n\geq 0}}$	A[n]*A[n + 1]*C[n + 1] > 0	Subscript[A, n]*Subscript[A, n + 1]*Subscript[C, n + 1] > 0	Skipped - no semantic math	Skipped - no semantic math	-	-
18.30#Ex1	${\displaystyle{\displaystyle p_{-1}(x;c)=0}}$ p_{-1}(x;c) = 0		p[- 1](x ; c) = 0	Subscript[p, - 1][x ; c] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
18.30#Ex2	${\displaystyle{\displaystyle p_{0}(x;c)=1}}$ p_{0}(x;c) = 1		p[0](x ; c) = 1	Subscript[p, 0][x ; c] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
18.30.E3	${\displaystyle{\displaystyle p_{n+1}(x;c)=(A_{n+c}x+B_{n+c})p_{n}(x;c)-C_{n+c}p_{n-1}(x;c)}}$ p_{n+1}(x;c) = (A_{n+c}x+B_{n+c})p_{n}(x;c)-C_{n+c}p_{n-1}(x;c)		p[n + 1](x ; c) = (A[n + c]*x + B[n + c])*p[n](x ; c)- C[n + c]*p[n - 1](x ; c)	Subscript[p, n + 1][x ; c] == (Subscript[A, n + c]*x + Subscript[B, n + c])*Subscript[p, n][x ; c]- Subscript[C, n + c]*Subscript[p, n - 1][x ; c]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.32.E1	${\displaystyle{\displaystyle w(x)=\exp\left(-Q(x)\right)}}$ w(x) = \exp@{-Q(x)}	${\displaystyle{\displaystyle-\infty<x,x<\infty}}$	w(x) = exp(- Q(x))	w[x] == Exp[- Q[x]]	Skipped - Unable to analyze test case: Null	Skipped - Unable to analyze test case: Null	-	-
18.33.E2	${\displaystyle{\displaystyle\phi_{n}(z)=\kappa_{n}z^{n}+\sum_{\ell=1}^{n}\kappa_{n,n-\ell}z^{n-\ell}}}$ \phi_{n}(z) = \kappa_{n}z^{n}+\sum_{\ell=1}^{n}\kappa_{n,n-\ell}z^{n-\ell}		phi[n](z) = kappa[n]*(z)^(n)+ sum(kappa[n , n - ell]*(z)^(n - ell), ell = 1..n)	Subscript[\[Phi], n][z] == Subscript[\[Kappa], n]*(z)^(n)+ Sum[Subscript[\[Kappa], n , n - \[ScriptL]]*(z)^(n - \[ScriptL]), {\[ScriptL], 1, n}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.33.E3	${\displaystyle{\displaystyle\phi_{n}^{*}(z)=z^{n}\overline{\phi_{n}({\overline{z}^{-1}})}}}$ \phi_{n}^{*}(z) = z^{n}\conj{\phi_{n}(\conj{z}^{-1})}		(phi[n])^(*)(z) = (z)^(n)* conjugate(phi[n]((conjugate(z))^(- 1)))	(Subscript[\[Phi], n])^(*)[z] == (z)^(n)* Conjugate[Subscript[\[Phi], n][(Conjugate[z])^(- 1)]]	Error	Failure	Skip - symbolical successful subtest	Error
18.33.E3	${\displaystyle{\displaystyle z^{n}\overline{\phi_{n}({\overline{z}^{-1}})}={\kappa_{n}}+\sum_{\ell=1}^{n}\overline{\kappa}_{n,n-\ell}z^{\ell}}}$ z^{n}\conj{\phi_{n}(\conj{z}^{-1})} = {\kappa_{n}}+\sum_{\ell=1}^{n}\conj{\kappa}_{n,n-\ell}z^{\ell}		(z)^(n)* conjugate(phi[n]((conjugate(z))^(- 1))) = kappa[n]+ sum(conjugate(kappa)[n , n - ell]*(z)^(ell), ell = 1..n)	(z)^(n)* Conjugate[Subscript[\[Phi], n][(Conjugate[z])^(- 1)]] == Subscript[\[Kappa], n]+ Sum[Subscript[Conjugate[\[Kappa]], n , n - \[ScriptL]]*(z)^\[ScriptL], {\[ScriptL], 1, n}, GenerateConditions->None]	Aborted	Failure	Error	Failed [300 / 300] Result: Plus[Complex[0.0, -0.9999999999999999], Times[Complex[-0.8660254037844387, -0.49999999999999994], Subscript[Complex[0.8660254037844387, -0.49999999999999994], 1, 0]]] Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[κ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Plus[Complex[0.1339745962155613, -0.49999999999999994], Times[Complex[-0.5000000000000001, -0.8660254037844386], Subscript[Complex[0.8660254037844387, -0.49999999999999994], 2, 0]], Times[Complex[-0.8660254037844387, -0.49999999999999994], Subscript[Complex[0.8660254037844387, -0.49999999999999994], 2, 1]]] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[κ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.33.E4	${\displaystyle{\displaystyle\kappa_{n}z\phi_{n}(z)=\kappa_{n+1}\phi_{n+1}(z)-\phi_{n+1}(0)\phi_{n+1}^{*}(z)}}$ \kappa_{n}z\phi_{n}(z) = \kappa_{n+1}\phi_{n+1}(z)-\phi_{n+1}(0)\phi_{n+1}^{*}(z)		kappa[n]*z*phi[n](z) = kappa[n + 1]*phi[n + 1](z)- phi[n + 1](0)* (phi[n + 1])^(*)(z)	Subscript[\[Kappa], n]*z*Subscript[\[Phi], n][z] == Subscript[\[Kappa], n + 1]*Subscript[\[Phi], n + 1][z]- Subscript[\[Phi], n + 1][0]* (Subscript[\[Phi], n + 1])^(*)[z]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.33.E5	${\displaystyle{\displaystyle\kappa_{n}\phi_{n+1}(z)=\kappa_{n+1}z\phi_{n}(z)+\phi_{n+1}(0)\phi_{n}^{*}(z)}}$ \kappa_{n}\phi_{n+1}(z) = \kappa_{n+1}z\phi_{n}(z)+\phi_{n+1}(0)\phi_{n}^{*}(z)		kappa[n]*phi[n + 1](z) = kappa[n + 1]*z*phi[n](z)+ phi[n + 1](0)* (phi[n])^(*)(z)	Subscript[\[Kappa], n]*Subscript[\[Phi], n + 1][z] == Subscript[\[Kappa], n + 1]*z*Subscript[\[Phi], n][z]+ Subscript[\[Phi], n + 1][0]* (Subscript[\[Phi], n])^(*)[z]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.33.E6	${\displaystyle{\displaystyle\kappa_{n}\phi_{n}(0)\phi_{n+1}(z)+\kappa_{n-1}\phi_{n+1}(0)z\phi_{n-1}(z)=\left(\kappa_{n}\phi_{n+1}(0)+\kappa_{n+1}\phi_{n}(0)z\right)\phi_{n}(z)}}$ \kappa_{n}\phi_{n}(0)\phi_{n+1}(z)+\kappa_{n-1}\phi_{n+1}(0)z\phi_{n-1}(z) = \left(\kappa_{n}\phi_{n+1}(0)+\kappa_{n+1}\phi_{n}(0)z\right)\phi_{n}(z)		kappa[n]*phi[n](0)* phi[n + 1](z)+ kappa[n - 1]*phi[n + 1](0)* z*phi[n - 1](z) = (kappa[n]*phi[n + 1](0)+ kappa[n + 1]*phi[n](0)* z)*phi[n](z)	Subscript[\[Kappa], n]*Subscript[\[Phi], n][0]* Subscript[\[Phi], n + 1][z]+ Subscript[\[Kappa], n - 1]*Subscript[\[Phi], n + 1][0]* z*Subscript[\[Phi], n - 1][z] == (Subscript[\[Kappa], n]*Subscript[\[Phi], n + 1][0]+ Subscript[\[Kappa], n + 1]*Subscript[\[Phi], n][0]* z)*Subscript[\[Phi], n][z]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.33#Ex1	${\displaystyle{\displaystyle w_{1}(x)=(1-x^{2})^{-\frac{1}{2}}w\left(x+\mathrm{i}(1-x^{2})^{\frac{1}{2}}\right)}}$ w_{1}(x) = (1-x^{2})^{-\frac{1}{2}}w\left(x+\iunit(1-x^{2})^{\frac{1}{2}}\right)		w[1](x) = (1 - (x)^(2))^(-(1)/(2))* w(x + I*(1 - (x)^(2))^((1)/(2)))	Subscript[w, 1][x] == (1 - (x)^(2))^(-Divide[1,2])* w[x + I*(1 - (x)^(2))^(Divide[1,2])]	Failure	Failure	Failed [300 / 300] Result: 1.128217713+1.045869600*I Test Values: {w = 1/2*3^(1/2)+1/2*I, x = 3/2, w[1] = 1/2*3^(1/2)+1/2*I} Result: -.9208203932+1.594907706*I Test Values: {w = 1/2*3^(1/2)+1/2*I, x = 3/2, w[1] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[1.1282177124267212, 1.0458696000777863] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[w, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.9208203932499366, 1.5949077057544443] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[w, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
18.33#Ex2	${\displaystyle{\displaystyle w_{2}(x)=(1-x^{2})^{\frac{1}{2}}w\left(x+\mathrm{i}(1-x^{2})^{\frac{1}{2}}\right)}}$ w_{2}(x) = (1-x^{2})^{\frac{1}{2}}w\left(x+\iunit(1-x^{2})^{\frac{1}{2}}\right)		w[2](x) = (1 - (x)^(2))^((1)/(2))* w(x + I*(1 - (x)^(2))^((1)/(2)))	Subscript[w, 2][x] == (1 - (x)^(2))^(Divide[1,2])* w[x + I*(1 - (x)^(2))^(Divide[1,2])]	Failure	Failure	Failed [300 / 300] Result: 1.512563597+.3801630000*I Test Values: {w = 1/2*3^(1/2)+1/2*I, x = 3/2, w[2] = 1/2*3^(1/2)+1/2*I} Result: -.5364745086+.9292011060*I Test Values: {w = 1/2*3^(1/2)+1/2*I, x = 3/2, w[2] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[1.5125635972390792, 0.38016299990276686] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[w, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.5364745084375786, 0.9292011055794249] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[w, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
18.33.E10	${\displaystyle{\displaystyle z^{-n}\phi_{2n}(z)={A_{n}p_{n}\left(\tfrac{1}{2}(z+z^{-1})\right)+B_{n}(z-z^{-1})q_{n-1}\left(\tfrac{1}{2}(z+z^{-1})\right)}}}$ z^{-n}\phi_{2n}(z) = {A_{n}p_{n}\left(\tfrac{1}{2}(z+z^{-1})\right)+B_{n}(z-z^{-1})q_{n-1}\left(\tfrac{1}{2}(z+z^{-1})\right)}		(z)^(- n)* phi[2*n](z) = A[n]*p[n]*((1)/(2)*(z + (z)^(- 1)))+ B[n]*(z - (z)^(- 1))*q[n - 1]*((1)/(2)*(z + (z)^(- 1)))	(z)^(- n)* Subscript[\[Phi], 2*n][z] == Subscript[A, n]*Subscript[p, n]*(Divide[1,2]*(z + (z)^(- 1)))+ Subscript[B, n]*(z - (z)^(- 1))*Subscript[q, n - 1]*(Divide[1,2]*(z + (z)^(- 1)))	Skipped - no semantic math	Skipped - no semantic math	-	-
18.33.E11	${\displaystyle{\displaystyle z^{-n+1}\phi_{2n-1}(z)={C_{n}p_{n}\left(\tfrac{1}{2}(z+z^{-1})\right)+D_{n}(z-z^{-1})q_{n-1}\left(\tfrac{1}{2}(z+z^{-1})\right)}}}$ z^{-n+1}\phi_{2n-1}(z) = {C_{n}p_{n}\left(\tfrac{1}{2}(z+z^{-1})\right)+D_{n}(z-z^{-1})q_{n-1}\left(\tfrac{1}{2}(z+z^{-1})\right)}		(z)^(- n + 1)* phi[2*n - 1](z) = C[n]*p[n]*((1)/(2)*(z + (z)^(- 1)))+ D[n]*(z - (z)^(- 1))*q[n - 1]*((1)/(2)*(z + (z)^(- 1)))	(z)^(- n + 1)* Subscript[\[Phi], 2*n - 1][z] == Subscript[C, n]*Subscript[p, n]*(Divide[1,2]*(z + (z)^(- 1)))+ Subscript[D, n]*(z - (z)^(- 1))*Subscript[q, n - 1]*(Divide[1,2]*(z + (z)^(- 1)))	Skipped - no semantic math	Skipped - no semantic math	-	-
18.33#Ex3	${\displaystyle{\displaystyle\phi_{n}(z)=z^{n}}}$ \phi_{n}(z) = z^{n}		phi[n](z) = (z)^(n)	Subscript[\[Phi], n][z] == (z)^(n)	Skipped - no semantic math	Skipped - no semantic math	-	-
18.33#Ex4	${\displaystyle{\displaystyle w(z)=1}}$ w(z) = 1		w(z) = 1	w[z] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
18.33.E13	${\displaystyle{\displaystyle\phi_{n}(z)=\sum_{\ell=0}^{n}\frac{{\left(\lambda+1\right)_{\ell}}{\left(\lambda\right)_{n-\ell}}}{\ell!\,(n-\ell)!}\,z^{\ell}}}$ \phi_{n}(z) = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda+1}{\ell}\Pochhammersym{\lambda}{n-\ell}}{\ell!\,(n-\ell)!}\,z^{\ell}		phi[n](z) = sum((pochhammer(lambda + 1, ell)*pochhammer(lambda, n - ell))/(factorial(ell)*factorial(n - ell))*(z)^(ell), ell = 0..n)	Subscript[\[Phi], n][z] == Sum[Divide[Pochhammer[\[Lambda]+ 1, \[ScriptL]]*Pochhammer[\[Lambda], n - \[ScriptL]],(\[ScriptL])!*(n - \[ScriptL])!]*(z)^\[ScriptL], {\[ScriptL], 0, n}, GenerateConditions->None]	Aborted	Failure	Failed [299 / 300] Result: -1.732050808-1.000000000*I Test Values: {lambda = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, phi[n] = 1/2*3^(1/2)+1/2*I, n = 1} Result: -.9330127026-4.482050809*I Test Values: {lambda = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, phi[n] = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-1.7320508075688772, -1.0] Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.9330127018922204, -4.482050807568885] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.33.E13	${\displaystyle{\displaystyle\sum_{\ell=0}^{n}\frac{{\left(\lambda+1\right)_{\ell}}{\left(\lambda\right)_{n-\ell}}}{\ell!\,(n-\ell)!}\,z^{\ell}=\frac{{\left(\lambda\right)_{n}}}{n!}{{}_{2}F_{1}}\left({-n,\lambda+1\atop-\lambda-n+1};z\right)}}$ \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda+1}{\ell}\Pochhammersym{\lambda}{n-\ell}}{\ell!\,(n-\ell)!}\,z^{\ell} = \frac{\Pochhammersym{\lambda}{n}}{n!}\genhyperF{2}{1}@@{-n,\lambda+1}{-\lambda-n+1}{z}		sum((pochhammer(lambda + 1, ell)*pochhammer(lambda, n - ell))/(factorial(ell)*factorial(n - ell))*(z)^(ell), ell = 0..n) = (pochhammer(lambda, n))/(factorial(n))*hypergeom([- n , lambda + 1], [- lambda - n + 1], z)	Sum[Divide[Pochhammer[\[Lambda]+ 1, \[ScriptL]]*Pochhammer[\[Lambda], n - \[ScriptL]],(\[ScriptL])!*(n - \[ScriptL])!]*(z)^\[ScriptL], {\[ScriptL], 0, n}, GenerateConditions->None] == Divide[Pochhammer[\[Lambda], n],(n)!]*HypergeometricPFQ[{- n , \[Lambda]+ 1}, {- \[Lambda]- n + 1}, z]	Aborted	Successful	Successful [Tested: 0]	Failed [21 / 210] Result: Indeterminate Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, -2]} Result: Indeterminate Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, -2]} ... skip entries to safe data
18.33#Ex5	${\displaystyle{\displaystyle w(z)=\left(1-\tfrac{1}{2}(z+z^{-1})\right)^{\lambda}}}$ w(z) = \left(1-\tfrac{1}{2}(z+z^{-1})\right)^{\lambda}		w(z) = (1 -(1)/(2)*(z + (z)^(- 1)))^(lambda)	w[z] == (1 -Divide[1,2]*(z + (z)^(- 1)))^\[Lambda]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.33#Ex6	${\displaystyle{\displaystyle w_{1}(x)=(1-x)^{\lambda-\frac{1}{2}}(1+x)^{-\frac{1}{2}}}}$ w_{1}(x) = (1-x)^{\lambda-\frac{1}{2}}(1+x)^{-\frac{1}{2}}		w[1](x) = (1 - x)^(lambda -(1)/(2))*(1 + x)^(-(1)/(2))	Subscript[w, 1][x] == (1 - x)^(\[Lambda]-Divide[1,2])*(1 + x)^(-Divide[1,2])	Skipped - no semantic math	Skipped - no semantic math	-	-
18.33#Ex7	${\displaystyle{\displaystyle w_{2}(x)=(1-x)^{\lambda+\frac{1}{2}}(1+x)^{\frac{1}{2}}}}$ w_{2}(x) = (1-x)^{\lambda+\frac{1}{2}}(1+x)^{\frac{1}{2}}	${\displaystyle{\displaystyle\lambda>-\tfrac{1}{2}}}$	w[2](x) = (1 - x)^(lambda +(1)/(2))*(1 + x)^((1)/(2))	Subscript[w, 2][x] == (1 - x)^(\[Lambda]+Divide[1,2])*(1 + x)^(Divide[1,2])	Skipped - no semantic math	Skipped - no semantic math	-	-
18.33.E15	${\displaystyle{\displaystyle\phi_{n}(z)=\sum_{\ell=0}^{n}\frac{\left(aq^{2};q^{2}\right)_{\ell}\left(a;q^{2}\right)_{n-\ell}}{\left(q^{2};q^{2}\right)_{\ell}\left(q^{2};q^{2}\right)_{n-\ell}}(q^{-1}z)^{\ell}}}$ \phi_{n}(z) = \sum_{\ell=0}^{n}\frac{\qPochhammer{aq^{2}}{q^{2}}{\ell}\qPochhammer{a}{q^{2}}{n-\ell}}{\qPochhammer{q^{2}}{q^{2}}{\ell}\qPochhammer{q^{2}}{q^{2}}{n-\ell}}(q^{-1}z)^{\ell}		phi[n](z) = sum((QPochhammer(a*(q)^(2), (q)^(2), ell)*QPochhammer(a, (q)^(2), n - ell))/(QPochhammer((q)^(2), (q)^(2), ell)*QPochhammer((q)^(2), (q)^(2), n - ell))*((q)^(- 1)* z)^(ell), ell = 0..n)	Subscript[\[Phi], n][z] == Sum[Divide[QPochhammer[a*(q)^(2), (q)^(2), \[ScriptL]]*QPochhammer[a, (q)^(2), n - \[ScriptL]],QPochhammer[(q)^(2), (q)^(2), \[ScriptL]]*QPochhammer[(q)^(2), (q)^(2), n - \[ScriptL]]]*((q)^(- 1)* z)^\[ScriptL], {\[ScriptL], 0, n}, GenerateConditions->None]	Aborted	Aborted	Error	Skipped - Because timed out
18.33.E15	${\displaystyle{\displaystyle\sum_{\ell=0}^{n}\frac{\left(aq^{2};q^{2}\right)_{\ell}\left(a;q^{2}\right)_{n-\ell}}{\left(q^{2};q^{2}\right)_{\ell}\left(q^{2};q^{2}\right)_{n-\ell}}(q^{-1}z)^{\ell}=\frac{\left(a;q^{2}\right)_{n}}{\left(q^{2};q^{2}\right)_{n}}{{}_{2}\phi_{1}}\left({aq^{2},q^{-2n}\atop a^{-1}q^{2-2n}};q^{2},\frac{qz}{a}\right)}}$ \sum_{\ell=0}^{n}\frac{\qPochhammer{aq^{2}}{q^{2}}{\ell}\qPochhammer{a}{q^{2}}{n-\ell}}{\qPochhammer{q^{2}}{q^{2}}{\ell}\qPochhammer{q^{2}}{q^{2}}{n-\ell}}(q^{-1}z)^{\ell} = \frac{\qPochhammer{a}{q^{2}}{n}}{\qPochhammer{q^{2}}{q^{2}}{n}}\qgenhyperphi{2}{1}@@{aq^{2},q^{-2n}}{a^{-1}q^{2-2n}}{q^{2}}{\frac{qz}{a}}		Error	Sum[Divide[QPochhammer[a*(q)^(2), (q)^(2), \[ScriptL]]*QPochhammer[a, (q)^(2), n - \[ScriptL]],QPochhammer[(q)^(2), (q)^(2), \[ScriptL]]*QPochhammer[(q)^(2), (q)^(2), n - \[ScriptL]]]*((q)^(- 1)* z)^\[ScriptL], {\[ScriptL], 0, n}, GenerateConditions->None] == Divide[QPochhammer[a, (q)^(2), n],QPochhammer[(q)^(2), (q)^(2), n]]*QHypergeometricPFQ[{a*(q)^(2), (q)^(- 2*n)},{(a)^(- 1)* (q)^(2 - 2*n)},(q)^(2),Divide[q*z,a]]	Missing Macro Error	Aborted	Skip - symbolical successful subtest	Skipped - Because timed out
18.34.E1	${\displaystyle{\displaystyle y_{n}\left(x;a\right)={{}_{2}F_{0}}\left({-n,n+a-1\atop-};-\frac{x}{2}\right)}}$ \Besselpolyy{n}@{x}{a} = \genhyperF{2}{0}@@{-n,n+a-1}{-}{-\frac{x}{2}}		Error	Pochhammer[n + a - 1, n] (x/2)^n Hypergeometric1F1[-n, -2 n - a + 2, 2/x] == HypergeometricPFQ[{- n , n + a - 1}, {-}, -Divide[x,2]]	Missing Macro Error	Failure	-	Error
18.34.E1	${\displaystyle{\displaystyle{{}_{2}F_{0}}\left({-n,n+a-1\atop-};-\frac{x}{2}\right)={\left(n+a-1\right)_{n}}\left(\frac{x}{2}\right)^{n}{{}_{1}F_{1}}\left({-n\atop-2n-a+2};\frac{2}{x}\right)}}$ \genhyperF{2}{0}@@{-n,n+a-1}{-}{-\frac{x}{2}} = \Pochhammersym{n+a-1}{n}\left(\frac{x}{2}\right)^{n}\genhyperF{1}{1}@@{-n}{-2n-a+2}{\frac{2}{x}}		hypergeom([- n , n + a - 1], [-], -(x)/(2)) = pochhammer(n + a - 1, n)*((x)/(2))^(n)* hypergeom([- n], [- 2*n - a + 2], (2)/(x))	HypergeometricPFQ[{- n , n + a - 1}, {-}, -Divide[x,2]] == Pochhammer[n + a - 1, n]*(Divide[x,2])^(n)* HypergeometricPFQ[{- n}, {- 2*n - a + 2}, Divide[2,x]]	Error	Failure	-	Error
18.34#Ex1	${\displaystyle{\displaystyle y_{n}(x)=y_{n}\left(x;2\right)}}$ y_{n}(x) = \Besselpolyy{n}@{x}{2}		Error	Subscript[y, n][x] == Pochhammer[n + 2 - 1, n] (x/2)^n Hypergeometric1F1[-n, -2 n - 2 + 2, 2/x]	Missing Macro Error	Failure	-	Failed [89 / 90] Result: Complex[-1.200961894323342, 0.7499999999999999] Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[Subscript[y, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-10.950961894323342, 0.7499999999999999] Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[Subscript[y, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.34#Ex2	${\displaystyle{\displaystyle\theta_{n}(x)=x^{n}y_{n}(x^{-1})}}$ \theta_{n}(x) = x^{n}y_{n}(x^{-1})		theta[n](x) = (x)^(n)* y[n]((x)^(- 1))	Subscript[\[Theta], n][x] == (x)^(n)* Subscript[y, n][(x)^(- 1)]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.34#Ex3	${\displaystyle{\displaystyle y_{n}(x;a,b)=y_{n}\left(2x/b;a\right)}}$ y_{n}(x;a,b) = \Besselpolyy{n}@{2x/b}{a}		Error	Subscript[y, n][x ; a , b] == Pochhammer[n + a - 1, n] (2*x/b/2)^n Hypergeometric1F1[-n, -2 n - a + 2, 2/2*x/b]	Translation Error	Translation Error	-	-
18.34#Ex4	${\displaystyle{\displaystyle\theta_{n}(x;a,b)=x^{n}y_{n}(x^{-1};a,b)}}$ \theta_{n}(x;a,b) = x^{n}y_{n}(x^{-1};a,b)		theta[n](x ; a , b) = (x)^(n)* y[n]((x)^(- 1); a , b)	Subscript[\[Theta], n][x ; a , b] == (x)^(n)* Subscript[y, n][(x)^(- 1); a , b]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.34.E4	${\displaystyle{\displaystyle y_{n+1}\left(x;a\right)=(A_{n}x+B_{n})y_{n}\left(x;a\right)-C_{n}y_{n-1}\left(x;a\right)}}$ \Besselpolyy{n+1}@{x}{a} = (A_{n}x+B_{n})\Besselpolyy{n}@{x}{a}-C_{n}\Besselpolyy{n-1}@{x}{a}		Error	Pochhammer[n + 1 + a - 1, n + 1] (x/2)^n + 1 Hypergeometric1F1[-n + 1, -2 n + 1 - a + 2, 2/x] == (Subscript[A, n]*x + Subscript[B, n])*Pochhammer[n + a - 1, n] (x/2)^n Hypergeometric1F1[-n, -2 n - a + 2, 2/x]-(Divide[- n*(2*n + a),(n + a - 1)*(2*n + a - 2)])*Pochhammer[n - 1 + a - 1, n - 1] (x/2)^n - 1 Hypergeometric1F1[-n - 1, -2 n - 1 - a + 2, 2/x]	Missing Macro Error	Aborted	-	Failed [300 / 300] Result: Complex[-1.0464966909469928, 0.15625000000000006] Test Values: {Rule[a, -1.5], Rule[n, 1], Rule[x, 1.5], Rule[Subscript[A, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[B, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-13.266992864557183, -0.13671874999999994] Test Values: {Rule[a, -1.5], Rule[n, 2], Rule[x, 1.5], Rule[Subscript[A, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[B, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.34.E7	${\displaystyle{\displaystyle x^{2}y_{n}''\left(x;a\right)+(ax+2)y_{n}'\left(x;a\right)-n(n+a-1)y_{n}\left(x;a\right)=0}}$ x^{2}\Besselpolyy{n}''@{x}{a}+(ax+2)\Besselpolyy{n}'@{x}{a}-n(n+a-1)\Besselpolyy{n}@{x}{a} = 0		Error	(x)^(2)* D[Pochhammer[n + a - 1, n] (x/2)^n Hypergeometric1F1[-n, -2 n - a + 2, 2/x], {x, 2}]+(a*x + 2)*D[Pochhammer[n + a - 1, n] (x/2)^n Hypergeometric1F1[-n, -2 n - a + 2, 2/x], {x, 1}]- n*(n + a - 1)*Pochhammer[n + a - 1, n] (x/2)^n Hypergeometric1F1[-n, -2 n - a + 2, 2/x] == 0	Missing Macro Error	Successful	-	Failed [9 / 54] Result: Indeterminate Test Values: {Rule[a, -2], Rule[n, 2], Rule[x, 1.5]} Result: Indeterminate Test Values: {Rule[a, -2], Rule[n, 3], Rule[x, 1.5]} ... skip entries to safe data
18.34.E8	${\displaystyle{\displaystyle\lim_{\alpha\to\infty}\frac{P^{(\alpha,a-\alpha-2)}_{n}\left(1+\alpha x\right)}{P^{(\alpha,a-\alpha-2)}_{n}\left(1\right)}=y_{n}\left(x;a\right)}}$ \lim_{\alpha\to\infty}\frac{\JacobipolyP{\alpha}{a-\alpha-2}{n}@{1+\alpha x}}{\JacobipolyP{\alpha}{a-\alpha-2}{n}@{1}} = \Besselpolyy{n}@{x}{a}		Error	Limit[Divide[JacobiP[n, \[Alpha], a - \[Alpha]- 2, 1 + \[Alpha]*x],JacobiP[n, \[Alpha], a - \[Alpha]- 2, 1]], \[Alpha] -> Infinity, GenerateConditions->None] == Pochhammer[n + a - 1, n] (x/2)^n Hypergeometric1F1[-n, -2 n - a + 2, 2/x]	Missing Macro Error	Aborted	-	Skipped - Because timed out
18.35.E4	${\displaystyle{\displaystyle\frac{{\left(\lambda-\mathrm{i}\tau_{a,b}(\theta)\right)_{n}}}{n!}e^{\mathrm{i}n\theta}\*{{}_{2}F_{1}}\left({-n,\lambda+\mathrm{i}\tau_{a,b}(\theta)\atop-n-\lambda+1+\mathrm{i}\tau_{a,b}(\theta)};e^{-2\mathrm{i}\theta}\right)=\sum_{\ell=0}^{n}\frac{{\left(\lambda+\mathrm{i}\tau_{a,b}(\theta)\right)_{\ell}}}{\ell!}\frac{{\left(\lambda-\mathrm{i}\tau_{a,b}(\theta)\right)_{n-\ell}}}{(n-\ell)!}e^{\mathrm{i}(n-2\ell)\theta}}}$ \frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n}}{n!}e^{\iunit n\theta}\*\genhyperF{2}{1}@@{-n,\lambda+\iunit\tau_{a,b}(\theta)}{-n-\lambda+1+\iunit\tau_{a,b}(\theta)}{e^{-2\iunit\theta}} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda+\iunit\tau_{a,b}(\theta)}{\ell}}{\ell!}\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n-\ell}}{(n-\ell)!}e^{\iunit(n-2\ell)\theta}	${\displaystyle{\displaystyle 0<\theta,\theta<\pi}}$	(pochhammer(lambda - I*((a*cos(theta)+ b)/(sin(theta))), n))/(factorial(n))*exp(I*n*theta)* hypergeom([- n , lambda + I*((a*cos(theta)+ b)/(sin(theta)))], [- n - lambda + 1 + I*((a*cos(theta)+ b)/(sin(theta)))], exp(- 2*I*theta)) = sum((pochhammer(lambda + I*((a*cos(theta)+ b)/(sin(theta))), ell))/(factorial(ell))*(pochhammer(lambda - I*((a*cos(theta)+ b)/(sin(theta))), n - ell))/(factorial(n - ell))*exp(I*(n - 2*ell)*theta), ell = 0..n)	Divide[Pochhammer[\[Lambda]- I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), n],(n)!]*Exp[I*n*\[Theta]]* HypergeometricPFQ[{- n , \[Lambda]+ I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]])}, {- n - \[Lambda]+ 1 + I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]])}, Exp[- 2*I*\[Theta]]] == Sum[Divide[Pochhammer[\[Lambda]+ I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), \[ScriptL]],(\[ScriptL])!]*Divide[Pochhammer[\[Lambda]- I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), n - \[ScriptL]],(n - \[ScriptL])!]*Exp[I*(n - 2*\[ScriptL])*\[Theta]], {\[ScriptL], 0, n}, GenerateConditions->None]	Error	Successful	-	Successful [Tested: 300]
18.35.E6	${\displaystyle{\displaystyle w^{(\lambda)}(\cos\theta;a,b)=\pi^{-1}\*2^{2\lambda-1}\*e^{(2\theta-\pi)\*\tau_{a,b}(\theta)}\*(\sin\theta)^{2\lambda-1}\*{\left|\Gamma\left(\lambda+\mathrm{i}\tau_{a,b}(\theta)\right)\right|^{2}}}}$ w^{(\lambda)}(\cos@@{\theta};a,b) = \pi^{-1}\*2^{2\lambda-1}\*e^{(2\theta-\pi)\*\tau_{a,b}(\theta)}\*(\sin@@{\theta})^{2\lambda-1}\*\abs{\EulerGamma@{\lambda+\iunit\tau_{a,b}(\theta)}}^{2}	${\displaystyle{\displaystyle a\geq b,b\geq-a,\lambda>-\frac{1}{2},0<\theta,\theta<\pi}}$	(w(cos(theta); a , b))^(lambda) = (Pi)^(- 1)* (2)^(2*lambda - 1)* exp((2*theta - Pi)*((a*cos(theta)+ b)/(sin(theta))))*(sin(theta))^(2*lambda - 1)* (abs(GAMMA(lambda + I*((a*cos(theta)+ b)/(sin(theta))))))^(2)	(w[Cos[\[Theta]]; a , b])^(\[Lambda]) == (Pi)^(- 1)* (2)^(2*\[Lambda]- 1)* Exp[(2*\[Theta]- Pi)*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]])]*(Sin[\[Theta]])^(2*\[Lambda]- 1)* (Abs[Gamma[\[Lambda]+ I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]])]])^(2)	Translation Error	Translation Error	-	-
18.38.E1	${\displaystyle{\displaystyle V_{n}(x)=\ifrac{2nH_{n+1}\left(x\right)H_{n-1}\left(x\right)}{(H_{n}\left(x\right))^{2}}}}$ V_{n}(x) = \ifrac{2n\HermitepolyH{n+1}@{x}\HermitepolyH{n-1}@{x}}{(\HermitepolyH{n}@{x})^{2}}		V[n](x) = (2*n*HermiteH(n + 1, x)*HermiteH(n - 1, x))/((HermiteH(n, x))^(2))	Subscript[V, n][x] == Divide[2*n*HermiteH[n + 1, x]*HermiteH[n - 1, x],(HermiteH[n, x])^(2)]	Failure	Aborted	Failed [90 / 90] Result: -.256517449+.7500000000*I Test Values: {x = 3/2, V[n] = 1/2*3^(1/2)+1/2*I, n = 1} Result: -.905043527+.7500000000*I Test Values: {x = 3/2, V[n] = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [90 / 90] Result: Complex[-0.25651744987889735, 0.7499999999999999] Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[Subscript[V, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.905043526976403, 0.7499999999999999] Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[Subscript[V, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.38.E3	${\displaystyle{\displaystyle\sum_{m=0}^{n}P^{(\alpha,0)}_{m}\left(x\right)\geq 0}}$ \sum_{m=0}^{n}\JacobipolyP{\alpha}{0}{m}@{x} \geq 0	${\displaystyle{\displaystyle-1\leq x,x\leq 1,\alpha>-1}}$	sum(JacobiP(m, alpha, 0, x), m = 0..n) >= 0	Sum[JacobiP[m, \[Alpha], 0, x], {m, 0, n}, GenerateConditions->None] >= 0	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 27]
18.39.E3	${\displaystyle{\displaystyle V(x)=\tfrac{1}{2}m\omega^{2}x^{2}}}$ V(x) = \tfrac{1}{2}m\omega^{2}x^{2}		V(x) = (1)/(2)*m*(omega)^(2)* (x)^(2)	V[x] == Divide[1,2]*m*\[Omega]^(2)* (x)^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
18.39.E5	${\displaystyle{\displaystyle\eta_{n}(x)=\pi^{-\frac{1}{4}}2^{-\frac{1}{2}n}(n!\,b)^{-\frac{1}{2}}H_{n}\left(x/b\right)e^{-x^{2}/2b^{2}}}}$ \eta_{n}(x) = \pi^{-\frac{1}{4}}2^{-\frac{1}{2}n}(n!\,b)^{-\frac{1}{2}}\HermitepolyH{n}@{x/b}e^{-x^{2}/2b^{2}}		eta[n](x) = (Pi)^(-(1)/(4))* (2)^(-(1)/(2)*n)*(factorial(n)*b)^(-(1)/(2))* HermiteH(n, x/b)*exp(- (x)^(2)/2*(b)^(2))	Subscript[\[Eta], n][x] == (Pi)^(-Divide[1,4])* (2)^(-Divide[1,2]*n)*((n)!*b)^(-Divide[1,2])* HermiteH[n, x/b]*Exp[- (x)^(2)/2*(b)^(2)]	Failure	Failure	Failed [300 / 300] Result: 1.299038106+.6809960435*I Test Values: {b = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, eta[n] = 1/2*3^(1/2)+1/2*I, n = 1} Result: 1.299038106+.7845019783*I Test Values: {b = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, eta[n] = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[1.299038105676658, 0.6809960434853285] Test Values: {Rule[b, -1.5], Rule[n, 1], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[η, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.299038105676658, 0.7845019782573356] Test Values: {Rule[b, -1.5], Rule[n, 2], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[η, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data