18.14

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
18.14.E1	${\displaystyle{\displaystyle|P^{(\alpha,\beta)}_{n}\left(x\right)|\leq P^{(\alpha,\beta)}_{n}\left(1\right)}}$ |\JacobipolyP{\alpha}{\beta}{n}@{x}| \leq \JacobipolyP{\alpha}{\beta}{n}@{1}	${\displaystyle{\displaystyle-1\leq x,x\leq 1,\alpha\geq\beta,\beta>-1}}$	abs(JacobiP(n, alpha, beta, x)) <= JacobiP(n, alpha, beta, 1)	Abs[JacobiP[n, \[Alpha], \[Beta], x]] <= JacobiP[n, \[Alpha], \[Beta], 1]	Failure	Failure	Successful [Tested: 9]	Successful [Tested: 9]
18.14.E1	${\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}\left(1\right)=\frac{{\left(\alpha+1\right)_{n}}}{n!}}}$ \JacobipolyP{\alpha}{\beta}{n}@{1} = \frac{\Pochhammersym{\alpha+1}{n}}{n!}	${\displaystyle{\displaystyle-1\leq x,x\leq 1,\alpha\geq\beta,\beta>-1}}$	JacobiP(n, alpha, beta, 1) = (pochhammer(alpha + 1, n))/(factorial(n))	JacobiP[n, \[Alpha], \[Beta], 1] == Divide[Pochhammer[\[Alpha]+ 1, n],(n)!]	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 9]
18.14.E2	${\displaystyle{\displaystyle|P^{(\alpha,\beta)}_{n}\left(x\right)|\leq|P^{(\alpha,\beta)}_{n}\left(-1\right)|=\frac{{\left(\beta+1\right)_{n}}}{n!}}}$ |\JacobipolyP{\alpha}{\beta}{n}@{x}| \leq |\JacobipolyP{\alpha}{\beta}{n}@{-1}|=\frac{\Pochhammersym{\beta+1}{n}}{n!}	${\displaystyle{\displaystyle-1\leq x,x\leq 1,\beta\geq\alpha,\alpha>-1}}$	abs(JacobiP(n, alpha, beta, x)) <= abs(JacobiP(n, alpha, beta, - 1)) = (pochhammer(beta + 1, n))/(factorial(n))	Abs[JacobiP[n, \[Alpha], \[Beta], x]] <= Abs[JacobiP[n, \[Alpha], \[Beta], - 1]] == Divide[Pochhammer[\[Beta]+ 1, n],(n)!]	Failure	Failure	Error	Failed [1 / 9] Result: False Test Values: {Rule[n, 1], Rule[x, 0.5], Rule[α, 2], Rule[β, Rational[1, 2]]}
18.14.E4	${\displaystyle{\displaystyle|C^{(\lambda)}_{n}\left(x\right)|\leq C^{(\lambda)}_{n}\left(1\right)}}$ |\ultrasphpoly{\lambda}{n}@{x}| \leq \ultrasphpoly{\lambda}{n}@{1}	${\displaystyle{\displaystyle-1\leq x,x\leq 1,\lambda>0}}$	abs(GegenbauerC(n, lambda, x)) <= GegenbauerC(n, lambda, 1)	Abs[GegenbauerC[n, \[Lambda], x]] <= GegenbauerC[n, \[Lambda], 1]	Failure	Failure	Successful [Tested: 9]	Successful [Tested: 9]
18.14.E4	${\displaystyle{\displaystyle C^{(\lambda)}_{n}\left(1\right)=\frac{{\left(2\lambda\right)_{n}}}{n!}}}$ \ultrasphpoly{\lambda}{n}@{1} = \frac{\Pochhammersym{2\lambda}{n}}{n!}	${\displaystyle{\displaystyle-1\leq x,x\leq 1,\lambda>0}}$	GegenbauerC(n, lambda, 1) = (pochhammer(2*lambda, n))/(factorial(n))	GegenbauerC[n, \[Lambda], 1] == Divide[Pochhammer[2*\[Lambda], n],(n)!]	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 9]
18.14.E5	${\displaystyle{\displaystyle|C^{(\lambda)}_{2m}\left(x\right)|\leq|C^{(\lambda)}_{2m}\left(0\right)|=\left|\frac{{\left(\lambda\right)_{m}}}{m!}\right|}}$ |\ultrasphpoly{\lambda}{2m}@{x}| \leq |\ultrasphpoly{\lambda}{2m}@{0}|=\left|\frac{\Pochhammersym{\lambda}{m}}{m!}\right|	${\displaystyle{\displaystyle-1\leq x,x\leq 1,-\tfrac{1}{2}<\lambda,\lambda<0}}$	abs(GegenbauerC(2*m, lambda, x)) <= abs(GegenbauerC(2*m, lambda, 0)) = abs((pochhammer(lambda, m))/(factorial(m)))	Abs[GegenbauerC[2*m, \[Lambda], x]] <= Abs[GegenbauerC[2*m, \[Lambda], 0]] == Abs[Divide[Pochhammer[\[Lambda], m],(m)!]]	Failure	Failure	Error	Skip - No test values generated
18.14.E6	${\displaystyle{\displaystyle|C^{(\lambda)}_{2m+1}\left(x\right)|<\frac{-2{\left(\lambda\right)_{m+1}}}{\left((2m+1)(2\lambda+2m+1)\right)^{\frac{1}{2}}m!}}}$ |\ultrasphpoly{\lambda}{2m+1}@{x}| < \frac{-2\Pochhammersym{\lambda}{m+1}}{\left((2m+1)(2\lambda+2m+1)\right)^{\frac{1}{2}}m!}	${\displaystyle{\displaystyle-1\leq x,x\leq 1,-\tfrac{1}{2}<\lambda,\lambda<0}}$	abs(GegenbauerC(2*m + 1, lambda, x)) < (- 2*pochhammer(lambda, m + 1))/(((2*m + 1)*(2*lambda + 2*m + 1))^((1)/(2))* factorial(m))	Abs[GegenbauerC[2*m + 1, \[Lambda], x]] < Divide[- 2*Pochhammer[\[Lambda], m + 1],((2*m + 1)*(2*\[Lambda]+ 2*m + 1))^(Divide[1,2])* (m)!]	Failure	Failure	Error	Skip - No test values generated
18.14.E7	${\displaystyle{\displaystyle(n+\lambda)^{1-\lambda}(1-x^{2})^{\frac{1}{2}\lambda}|C^{(\lambda)}_{n}\left(x\right)|<\frac{2^{1-\lambda}}{\Gamma\left(\lambda\right)}}}$ (n+\lambda)^{1-\lambda}(1-x^{2})^{\frac{1}{2}\lambda}|\ultrasphpoly{\lambda}{n}@{x}| < \frac{2^{1-\lambda}}{\EulerGamma@{\lambda}}	${\displaystyle{\displaystyle-1\leq x,x\leq 1,0<\lambda,\lambda<1,\Re(\lambda)>0}}$	(n + lambda)^(1 - lambda)*(1 - (x)^(2))^((1)/(2)*lambda)*abs(GegenbauerC(n, lambda, x)) < ((2)^(1 - lambda))/(GAMMA(lambda))	(n + \[Lambda])^(1 - \[Lambda])*(1 - (x)^(2))^(Divide[1,2]*\[Lambda])*Abs[GegenbauerC[n, \[Lambda], x]] < Divide[(2)^(1 - \[Lambda]),Gamma[\[Lambda]]]	Skipped - Unable to analyze test case: Null	Skipped - Unable to analyze test case: Null	-	-
18.14.E8	${\displaystyle{\displaystyle e^{-\frac{1}{2}x}\left|L^{(\alpha)}_{n}\left(x\right)\right|\leq L^{(\alpha)}_{n}\left(0\right)}}$ e^{-\frac{1}{2}x}\left|\LaguerrepolyL[\alpha]{n}@{x}\right| \leq \LaguerrepolyL[\alpha]{n}@{0}	${\displaystyle{\displaystyle 0\leq x,x<\infty,\alpha\geq 0}}$	exp(-(1)/(2)*x)*abs(LaguerreL(n, alpha, x)) <= LaguerreL(n, alpha, 0)	Exp[-Divide[1,2]*x]*Abs[LaguerreL[n, \[Alpha], x]] <= LaguerreL[n, \[Alpha], 0]	Missing Macro Error	Failure	-	Successful [Tested: 27]
18.14.E8	${\displaystyle{\displaystyle L^{(\alpha)}_{n}\left(0\right)=\frac{{\left(\alpha+1\right)_{n}}}{n!}}}$ \LaguerrepolyL[\alpha]{n}@{0} = \frac{\Pochhammersym{\alpha+1}{n}}{n!}	${\displaystyle{\displaystyle 0\leq x,x<\infty,\alpha\geq 0}}$	LaguerreL(n, alpha, 0) = (pochhammer(alpha + 1, n))/(factorial(n))	LaguerreL[n, \[Alpha], 0] == Divide[Pochhammer[\[Alpha]+ 1, n],(n)!]	Missing Macro Error	Successful	-	Successful [Tested: 9]
18.14.E9	${\displaystyle{\displaystyle\frac{1}{(2^{n}n!)^{\frac{1}{2}}}e^{-\frac{1}{2}x^{2}}|H_{n}\left(x\right)|\leq 1}}$ \frac{1}{(2^{n}n!)^{\frac{1}{2}}}e^{-\frac{1}{2}x^{2}}|\HermitepolyH{n}@{x}| \leq 1	${\displaystyle{\displaystyle-\infty<x,x<\infty}}$	(1)/(((2)^(n)* factorial(n))^((1)/(2)))*exp(-(1)/(2)*(x)^(2))*abs(HermiteH(n, x)) <= 1	Divide[1,((2)^(n)* (n)!)^(Divide[1,2])]*Exp[-Divide[1,2]*(x)^(2)]*Abs[HermiteH[n, x]] <= 1	Failure	Failure	Successful [Tested: 9]	Successful [Tested: 9]
18.14.E10	${\displaystyle{\displaystyle(P_{n}\left(x\right))^{2}\geq P_{n-1}\left(x\right)P_{n+1}\left(x\right)}}$ (\LegendrepolyP{n}@{x})^{2} \geq \LegendrepolyP{n-1}@{x}\LegendrepolyP{n+1}@{x}	${\displaystyle{\displaystyle-1\leq x,x\leq 1}}$	(LegendreP(n, x))^(2) >= LegendreP(n - 1, x)*LegendreP(n + 1, x)	(LegendreP[n, x])^(2) >= LegendreP[n - 1, x]*LegendreP[n + 1, x]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
18.14.E11	${\displaystyle{\displaystyle(R_{n}(x))^{2}\geq R_{n-1}(x)R_{n+1}(x)}}$ (R_{n}(x))^{2} \geq R_{n-1}(x)R_{n+1}(x)	${\displaystyle{\displaystyle-1\leq x,x\leq 1,\beta\geq\alpha,\alpha>-1}}$	(R[n](x))^(2) >= R[n - 1](x)* R[n + 1](x)	(Subscript[R, n][x])^(2) >= Subscript[R, n - 1][x]* Subscript[R, n + 1][x]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.14.E12	${\displaystyle{\displaystyle(L^{(\alpha)}_{n}\left(x\right))^{2}\geq L^{(\alpha)}_{n-1}\left(x\right)L^{(\alpha)}_{n+1}\left(x\right)}}$ (\LaguerrepolyL[\alpha]{n}@{x})^{2} \geq \LaguerrepolyL[\alpha]{n-1}@{x}\LaguerrepolyL[\alpha]{n+1}@{x}	${\displaystyle{\displaystyle 0\leq x,x<\infty,\alpha\geq 0}}$	(LaguerreL(n, alpha, x))^(2) >= LaguerreL(n - 1, alpha, x)*LaguerreL(n + 1, alpha, x)	(LaguerreL[n, \[Alpha], x])^(2) >= LaguerreL[n - 1, \[Alpha], x]*LaguerreL[n + 1, \[Alpha], x]	Missing Macro Error	Failure	-	Successful [Tested: 27]
18.14.E13	${\displaystyle{\displaystyle(H_{n}\left(x\right))^{2}\geq H_{n-1}\left(x\right)H_{n+1}\left(x\right)}}$ (\HermitepolyH{n}@{x})^{2} \geq \HermitepolyH{n-1}@{x}\HermitepolyH{n+1}@{x}	${\displaystyle{\displaystyle-\infty<x,x<\infty}}$	(HermiteH(n, x))^(2) >= HermiteH(n - 1, x)*HermiteH(n + 1, x)	(HermiteH[n, x])^(2) >= HermiteH[n - 1, x]*HermiteH[n + 1, x]	Failure	Failure	Successful [Tested: 9]	Successful [Tested: 9]
18.14.E14	${\displaystyle{\displaystyle-1=x_{n,0}}}$ -1 = x_{n,0}		- 1 = x[n , 0]	- 1 == Subscript[x, n , 0]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.14.E15	${\displaystyle{\displaystyle x_{n,m}\leq(\beta-\alpha)/(\alpha+\beta+1)\leq x_{n,m+1}}}$ x_{n,m} \leq (\beta-\alpha)/(\alpha+\beta+1)\leq x_{n,m+1}		x[n , m] <= (beta - alpha)/(alpha + beta + 1) <= x[n , m + 1]	Subscript[x, n , m] <= (\[Beta]- \[Alpha])/(\[Alpha]+ \[Beta]+ 1) <= Subscript[x, n , m + 1]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.14#Ex1	${\displaystyle{\displaystyle|P^{(\alpha,\beta)}_{n}\left(x_{n,0}\right)|>|P^{(\alpha,\beta)}_{n}\left(x_{n,1}\right)|}}$ |\JacobipolyP{\alpha}{\beta}{n}@{x_{n,0}}| > |\JacobipolyP{\alpha}{\beta}{n}@{x_{n,1}}|		abs(JacobiP(n, alpha, beta, x[n , 0])) > abs(JacobiP(n, alpha, beta, x[n , 1]))	Abs[JacobiP[n, \[Alpha], \[Beta], Subscript[x, n , 0]]] > Abs[JacobiP[n, \[Alpha], \[Beta], Subscript[x, n , 1]]]	Failure	Failure	Failed [184 / 300] Result: 2.500000000 < 2.500000000 Test Values: {alpha = 3/2, beta = 3/2, x[n,0] = 1/2*3^(1/2)+1/2*I, x[n,1] = 1/2*3^(1/2)+1/2*I, n = 1} Result: 4.871793818 < 4.871793818 Test Values: {alpha = 3/2, beta = 3/2, x[n,0] = 1/2*3^(1/2)+1/2*I, x[n,1] = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [184 / 300] Result: False Test Values: {Rule[n, 1], Rule[α, 1.5], Rule[β, 1.5], Rule[Subscript[x, n, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, n, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: False Test Values: {Rule[n, 2], Rule[α, 1.5], Rule[β, 1.5], Rule[Subscript[x, n, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, n, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.14#Ex2	${\displaystyle{\displaystyle|P^{(\alpha,\beta)}_{n}\left(x_{n,n}\right)|>|P^{(\alpha,\beta)}_{n}\left(x_{n,n-1}\right)|}}$ |\JacobipolyP{\alpha}{\beta}{n}@{x_{n,n}}| > |\JacobipolyP{\alpha}{\beta}{n}@{x_{n,n-1}}|	${\displaystyle{\displaystyle\alpha>-\tfrac{1}{2},\beta>-\tfrac{1}{2}.}}$	abs(JacobiP(n, alpha, beta, x[n , n])) > abs(JacobiP(n, alpha, beta, x[n , n - 1]))	Abs[JacobiP[n, \[Alpha], \[Beta], Subscript[x, n , n]]] > Abs[JacobiP[n, \[Alpha], \[Beta], Subscript[x, n , n - 1]]]	Error	Failure	-	Skip - No test values generated
18.14#Ex3	${\displaystyle{\displaystyle|P^{(\alpha,\beta)}_{n}\left(x_{n,0}\right)|<|P^{(\alpha,\beta)}_{n}\left(x_{n,1}\right)|}}$ |\JacobipolyP{\alpha}{\beta}{n}@{x_{n,0}}| < |\JacobipolyP{\alpha}{\beta}{n}@{x_{n,1}}|		abs(JacobiP(n, alpha, beta, x[n , 0])) < abs(JacobiP(n, alpha, beta, x[n , 1]))	Abs[JacobiP[n, \[Alpha], \[Beta], Subscript[x, n , 0]]] < Abs[JacobiP[n, \[Alpha], \[Beta], Subscript[x, n , 1]]]	Failure	Failure	Failed [184 / 300] Result: 2.500000000 < 2.500000000 Test Values: {alpha = 3/2, beta = 3/2, x[n,0] = 1/2*3^(1/2)+1/2*I, x[n,1] = 1/2*3^(1/2)+1/2*I, n = 1} Result: 4.871793820 < 4.871793820 Test Values: {alpha = 3/2, beta = 3/2, x[n,0] = 1/2*3^(1/2)+1/2*I, x[n,1] = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [184 / 300] Result: False Test Values: {Rule[n, 1], Rule[α, 1.5], Rule[β, 1.5], Rule[Subscript[x, n, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, n, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: False Test Values: {Rule[n, 2], Rule[α, 1.5], Rule[β, 1.5], Rule[Subscript[x, n, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, n, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.14#Ex4	${\displaystyle{\displaystyle|P^{(\alpha,\beta)}_{n}\left(x_{n,n}\right)|<|P^{(\alpha,\beta)}_{n}\left(x_{n,n-1}\right)|}}$ |\JacobipolyP{\alpha}{\beta}{n}@{x_{n,n}}| < |\JacobipolyP{\alpha}{\beta}{n}@{x_{n,n-1}}|	${\displaystyle{\displaystyle-1<\alpha,\alpha<-\tfrac{1}{2},-1<\beta,\beta<-\tfrac{1}{2}.}}$	abs(JacobiP(n, alpha, beta, x[n , n])) < abs(JacobiP(n, alpha, beta, x[n , n - 1]))	Abs[JacobiP[n, \[Alpha], \[Beta], Subscript[x, n , n]]] < Abs[JacobiP[n, \[Alpha], \[Beta], Subscript[x, n , n - 1]]]	Error	Failure	-	Skip - No test values generated
18.14.E18	${\displaystyle{\displaystyle|P^{(\alpha,\beta)}_{n}\left(x_{n,0}\right)|<|P^{(\alpha,\beta)}_{n}\left(x_{n,1}\right)|}}$ |\JacobipolyP{\alpha}{\beta}{n}@{x_{n,0}}| < |\JacobipolyP{\alpha}{\beta}{n}@{x_{n,1}}|	${\displaystyle{\displaystyle-1<\beta,\beta\leq-\tfrac{1}{2}}}$	abs(JacobiP(n, alpha, beta, x[n , 0])) < abs(JacobiP(n, alpha, beta, x[n , 1]))	Abs[JacobiP[n, \[Alpha], \[Beta], Subscript[x, n , 0]]] < Abs[JacobiP[n, \[Alpha], \[Beta], Subscript[x, n , 1]]]	Failure	Failure	Error	Skip - No test values generated
18.14.E19	${\displaystyle{\displaystyle|P^{(\alpha,\beta)}_{n}\left(x_{n,0}\right)|>|P^{(\alpha,\beta)}_{n}\left(x_{n,1}\right)|}}$ |\JacobipolyP{\alpha}{\beta}{n}@{x_{n,0}}| > |\JacobipolyP{\alpha}{\beta}{n}@{x_{n,1}}|	${\displaystyle{\displaystyle-1<\alpha,\alpha\leq-\tfrac{1}{2}}}$	abs(JacobiP(n, alpha, beta, x[n , 0])) > abs(JacobiP(n, alpha, beta, x[n , 1]))	Abs[JacobiP[n, \[Alpha], \[Beta], Subscript[x, n , 0]]] > Abs[JacobiP[n, \[Alpha], \[Beta], Subscript[x, n , 1]]]	Failure	Failure	Error	Skip - No test values generated
18.14.E20	${\displaystyle{\displaystyle\left|\frac{P^{(\alpha,\beta)}_{n}\left(x_{n,n-m}\right)}{P^{(\alpha,\beta)}_{n}\left(1\right)}\right|>\left|\frac{P^{(\alpha,\beta)}_{n+1}\left(x_{n+1,n-m+1}\right)}{P^{(\alpha,\beta)}_{n+1}\left(1\right)}\right|}}$ \left|\frac{\JacobipolyP{\alpha}{\beta}{n}@{x_{n,n-m}}}{\JacobipolyP{\alpha}{\beta}{n}@{1}}\right| > \left|\frac{\JacobipolyP{\alpha}{\beta}{n+1}@{x_{n+1,n-m+1}}}{\JacobipolyP{\alpha}{\beta}{n+1}@{1}}\right|	${\displaystyle{\displaystyle\alpha=\beta,\beta>-\tfrac{1}{2},m=1}}$	abs((JacobiP(n, alpha, beta, x[n , n - m]))/(JacobiP(n, alpha, beta, 1))) > abs((JacobiP(n + 1, alpha, beta, x[n + 1 , n - m + 1]))/(JacobiP(n + 1, alpha, beta, 1)))	Abs[Divide[JacobiP[n, \[Alpha], \[Beta], Subscript[x, n , n - m]],JacobiP[n, \[Alpha], \[Beta], 1]]] > Abs[Divide[JacobiP[n + 1, \[Alpha], \[Beta], Subscript[x, n + 1 , n - m + 1]],JacobiP[n + 1, \[Alpha], \[Beta], 1]]]	Failure	Failure	Failed [188 / 300] Result: 1.113552873 < 1.000000000 Test Values: {alpha = 3/2, beta = 3/2, x[n,n-m] = 1/2*3^(1/2)+1/2*I, x[n+1,n-m+1] = 1/2*3^(1/2)+1/2*I, m = 1, n = 1} Result: 1.400000001 < 1.113552873 Test Values: {alpha = 3/2, beta = 3/2, x[n,n-m] = 1/2*3^(1/2)+1/2*I, x[n+1,n-m+1] = 1/2*3^(1/2)+1/2*I, m = 1, n = 2} ... skip entries to safe data	Failed [234 / 300] Result: False Test Values: {Rule[m, 1], Rule[n, 1], Rule[α, 1.5], Rule[β, 1.5], Rule[Subscript[x, n, Plus[Times[-1, m], n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, Plus[1, n], Plus[1, Times[-1, m], n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: False Test Values: {Rule[m, 1], Rule[n, 2], Rule[α, 1.5], Rule[β, 1.5], Rule[Subscript[x, n, Plus[Times[-1, m], n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, Plus[1, n], Plus[1, Times[-1, m], n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.14.E21	${\displaystyle{\displaystyle 0=x_{n,0}}}$ 0 = x_{n,0}		0 = x[n , 0]	0 == Subscript[x, n , 0]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.14.E22	${\displaystyle{\displaystyle x_{n,m}\leq\alpha+\tfrac{1}{2}}}$ x_{n,m} \leq \alpha+\tfrac{1}{2}		x[n , m] <= alpha +(1)/(2)	Subscript[x, n , m] <= \[Alpha]+Divide[1,2]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.14#Ex5	${\displaystyle{\displaystyle|L^{(\alpha)}_{n}\left(x_{n,0}\right)|>|L^{(\alpha)}_{n}\left(x_{n,1}\right)|}}$ |\LaguerrepolyL[\alpha]{n}@{x_{n,0}}| > |\LaguerrepolyL[\alpha]{n}@{x_{n,1}}|		abs(LaguerreL(n, alpha, x[n , 0])) > abs(LaguerreL(n, alpha, x[n , 1]))	Abs[LaguerreL[n, \[Alpha], Subscript[x, n , 0]]] > Abs[LaguerreL[n, \[Alpha], Subscript[x, n , 1]]]	Missing Macro Error	Failure	-	Failed [165 / 300] Result: False Test Values: {Rule[n, 1], Rule[α, 1.5], Rule[Subscript[x, n, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, n, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: False Test Values: {Rule[n, 2], Rule[α, 1.5], Rule[Subscript[x, n, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, n, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.14#Ex6	${\displaystyle{\displaystyle|L^{(\alpha)}_{n}\left(x_{n,n-1}\right)|>|L^{(\alpha)}_{n}\left(x_{n,n-2}\right)|}}$ |\LaguerrepolyL[\alpha]{n}@{x_{n,n-1}}| > |\LaguerrepolyL[\alpha]{n}@{x_{n,n-2}}|		abs(LaguerreL(n, alpha, x[n , n - 1])) > abs(LaguerreL(n, alpha, x[n , n - 2]))	Abs[LaguerreL[n, \[Alpha], Subscript[x, n , n - 1]]] > Abs[LaguerreL[n, \[Alpha], Subscript[x, n , n - 2]]]	Missing Macro Error	Failure	-	Failed [165 / 300] Result: False Test Values: {Rule[n, 1], Rule[α, 1.5], Rule[Subscript[x, n, Plus[-2, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, n, Plus[-1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: False Test Values: {Rule[n, 2], Rule[α, 1.5], Rule[Subscript[x, n, Plus[-2, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, n, Plus[-1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.14.E24	${\displaystyle{\displaystyle|L^{(\alpha)}_{n}\left(x_{n,0}\right)|<|L^{(\alpha)}_{n}\left(x_{n,1}\right)|}}$ |\LaguerrepolyL[\alpha]{n}@{x_{n,0}}| < |\LaguerrepolyL[\alpha]{n}@{x_{n,1}}|		abs(LaguerreL(n, alpha, x[n , 0])) < abs(LaguerreL(n, alpha, x[n , 1]))	Abs[LaguerreL[n, \[Alpha], Subscript[x, n , 0]]] < Abs[LaguerreL[n, \[Alpha], Subscript[x, n , 1]]]	Missing Macro Error	Failure	-	Failed [165 / 300] Result: False Test Values: {Rule[n, 1], Rule[α, 1.5], Rule[Subscript[x, n, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, n, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: False Test Values: {Rule[n, 2], Rule[α, 1.5], Rule[Subscript[x, n, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, n, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data