2.11

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
2.11.E1	${\displaystyle{\displaystyle I(m)=\int_{0}^{\pi}\frac{\cos\left(mt\right)}{t^{2}+1}\mathrm{d}t}}$ I(m) = \int_{0}^{\pi}\frac{\cos@{mt}}{t^{2}+1}\diff{t}		I(m) = int((cos(m*t))/((t)^(2)+ 1), t = 0..Pi)	I[m] == Integrate[Divide[Cos[m*t],(t)^(2)+ 1], {t, 0, Pi}, GenerateConditions->None]	Failure	Failure	Failed [30 / 30] Result: 2.012164326+2.811364624*I Test Values: {I = 1/2*3^(1/2)+1/2*I, m = 1} Result: 3.764776118+6.449767277*I Test Values: {I = 1/2*3^(1/2)+1/2*I, m = 2} Result: 10.44871992+12.82571836*I Test Values: {I = 1/2*3^(1/2)+1/2*I, m = 3} Result: -.5451540752-.6604650959*I Test Values: {I = -1/2+1/2*I*3^(1/2), m = 1} ... skip entries to safe data	Failed [9 / 9] Result: Complex[3.1301272053762923, 2.7021954356714506] Test Values: {Rule[Complex[0, 1], 1], Rule[m, 1]} Result: Complex[7.946986696458338, 4.871470912282225] Test Values: {Rule[Complex[0, 1], 1], Rule[m, 2]} ... skip entries to safe data
2.11#Ex1	${\displaystyle{\displaystyle q_{1}(t)=-\frac{2t}{(t^{2}+1)^{2}}}}$ q_{1}(t) = -\frac{2t}{(t^{2}+1)^{2}}		q[1](t) = -(2*t)/(((t)^(2)+ 1)^(2))	Subscript[q, 1][t] == -Divide[2*t,((t)^(2)+ 1)^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11#Ex2	${\displaystyle{\displaystyle q_{2}(t)=\frac{24(t^{3}-t)}{(t^{2}+1)^{4}}}}$ q_{2}(t) = \frac{24(t^{3}-t)}{(t^{2}+1)^{4}}		q[2](t) = (24*((t)^(3)- t))/(((t)^(2)+ 1)^(4))	Subscript[q, 2][t] == Divide[24*((t)^(3)- t),((t)^(2)+ 1)^(4)]	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11#Ex3	${\displaystyle{\displaystyle q_{3}(t)=-\frac{240(3t^{5}-10t^{3}+3t)}{(t^{2}+1)^{6}}}}$ q_{3}(t) = -\frac{240(3t^{5}-10t^{3}+3t)}{(t^{2}+1)^{6}}		q[3](t) = -(240*(3*(t)^(5)- 10*(t)^(3)+ 3*t))/(((t)^(2)+ 1)^(6))	Subscript[q, 3][t] == -Divide[240*(3*(t)^(5)- 10*(t)^(3)+ 3*t),((t)^(2)+ 1)^(6)]	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11.E5	${\displaystyle{\displaystyle E_{p}\left(z\right)=\frac{e^{-z}z^{p-1}}{\Gamma\left(p\right)}\int_{0}^{\infty}\frac{e^{-zt}t^{p-1}}{1+t}\mathrm{d}t}}$ \genexpintE{p}@{z} = \frac{e^{-z}z^{p-1}}{\EulerGamma@{p}}\int_{0}^{\infty}\frac{e^{-zt}t^{p-1}}{1+t}\diff{t}	${\displaystyle{\displaystyle\Re p>0}}$	Ei(p, z) = (exp(- z)*(z)^(p - 1))/(GAMMA(p))*int((exp(- z*t)*(t)^(p - 1))/(1 + t), t = 0..infinity)	ExpIntegralE[p, z] == Divide[Exp[- z]*(z)^(p - 1),Gamma[p]]*Integrate[Divide[Exp[- z*t]*(t)^(p - 1),1 + t], {t, 0, Infinity}, GenerateConditions->None]	Successful	Successful	-	Successful [Tested: 35]
2.11.E8	${\displaystyle{\displaystyle n=\rho-p+\alpha}}$ n = \rho-p+\alpha		n = rho - p + alpha	n == \[Rho]- p + \[Alpha]	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11.E9	${\displaystyle{\displaystyle\frac{1}{1+t}=\sum_{s=0}^{n-1}(-1)^{s}t^{s}+(-1)^{n}\frac{t^{n}}{1+t}}}$ \frac{1}{1+t} = \sum_{s=0}^{n-1}(-1)^{s}t^{s}+(-1)^{n}\frac{t^{n}}{1+t}		(1)/(1 + t) = sum((- 1)^(s)* (t)^(s), s = 0..n - 1)+(- 1)^(n)*((t)^(n))/(1 + t)	Divide[1,1 + t] == Sum[(- 1)^(s)* (t)^(s), {s, 0, n - 1}, GenerateConditions->None]+(- 1)^(n)*Divide[(t)^(n),1 + t]	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11.E11	${\displaystyle{\displaystyle\frac{e^{-z}}{2\pi}\int_{0}^{\infty}\frac{e^{-zt}t^{n+p-1}}{1+t}\mathrm{d}t=\frac{\Gamma\left(n+p\right)}{2\pi}\frac{E_{n+p}\left(z\right)}{z^{n+p-1}}}}$ \frac{e^{-z}}{2\pi}\int_{0}^{\infty}\frac{e^{-zt}t^{n+p-1}}{1+t}\diff{t} = \frac{\EulerGamma@{n+p}}{2\pi}\frac{\genexpintE{n+p}@{z}}{z^{n+p-1}}	${\displaystyle{\displaystyle\Re(n+p)>0}}$	(exp(- z))/(2*Pi)*int((exp(- z*t)*(t)^(n + p - 1))/(1 + t), t = 0..infinity) = (GAMMA(n + p))/(2*Pi)*(Ei(n + p, z))/((z)^(n + p - 1))	Divide[Exp[- z],2*Pi]*Integrate[Divide[Exp[- z*t]*(t)^(n + p - 1),1 + t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[n + p],2*Pi]*Divide[ExpIntegralE[n + p, z],(z)^(n + p - 1)]	Successful	Aborted	-	Successful [Tested: 189]
2.11.E14	${\displaystyle{\displaystyle a_{2}(\theta,\alpha)=\frac{1}{12}(6\alpha^{2}-6\alpha+1)-\frac{\alpha}{1+e^{i\theta}}+\frac{1}{(1+e^{i\theta})^{2}}}}$ a_{2}(\theta,\alpha) = \frac{1}{12}(6\alpha^{2}-6\alpha+1)-\frac{\alpha}{1+e^{i\theta}}+\frac{1}{(1+e^{i\theta})^{2}}		a[2](theta , alpha) = (1)/(12)*(6*(alpha)^(2)- 6*alpha + 1)-(alpha)/(1 + exp(I*theta))+(1)/((1 + exp(I*theta))^(2))	Subscript[a, 2][\[Theta], \[Alpha]] == Divide[1,12]*(6*\[Alpha]^(2)- 6*\[Alpha]+ 1)-Divide[\[Alpha],1 + Exp[I*\[Theta]]]+Divide[1,(1 + Exp[I*\[Theta]])^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11.E16	${\displaystyle{\displaystyle c(\theta)=\sqrt{2(1+e^{i\theta}+i(\theta-\pi))}}}$ c(\theta) = \sqrt{2(1+e^{i\theta}+i(\theta-\pi))}		c(theta) = sqrt(2*(1 + exp(I*theta)+ I*(theta - Pi)))	c[\[Theta]] == Sqrt[2*(1 + Exp[I*\[Theta]]+ I*(\[Theta]- Pi))]	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11.E17	${\displaystyle{\displaystyle h_{2s}(\theta,\alpha)=\frac{e^{i\alpha(\pi-\theta)}}{1+e^{-i\theta}}a_{2s}(\theta,\alpha)+(-1)^{s-1}i\frac{1\cdot 3\cdot 5\cdot\cdot\cdot(2s-1)}{(c(\theta))^{2s+1}}}}$ h_{2s}(\theta,\alpha) = \frac{e^{i\alpha(\pi-\theta)}}{1+e^{-i\theta}}a_{2s}(\theta,\alpha)+(-1)^{s-1}i\frac{1\cdot 3\cdot 5\cdot\cdot\cdot(2s-1)}{(c(\theta))^{2s+1}}		h[2*s](theta , alpha) = (exp(I*alpha*(Pi - theta)))/(1 + exp(- I*theta))*a[2*s](theta , alpha)+(- 1)^(s - 1)* I*(1 * 3 * 5 * * *(2*s - 1))/((c(theta))^(2*s + 1))	Subscript[h, 2*s][\[Theta], \[Alpha]] == Divide[Exp[I*\[Alpha]*(Pi - \[Theta])],1 + Exp[- I*\[Theta]]]*Subscript[a, 2*s][\[Theta], \[Alpha]]+(- 1)^(s - 1)* I*Divide[1 * 3 * 5 * * *(2*s - 1),(c[\[Theta]])^(2*s + 1)]	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11.E18	${\displaystyle{\displaystyle h_{0}(\theta,\alpha)=\frac{e^{i\alpha(\pi-\theta)}}{1+e^{-i\theta}}-\frac{i}{c(\theta)}}}$ h_{0}(\theta,\alpha) = \frac{e^{i\alpha(\pi-\theta)}}{1+e^{-i\theta}}-\frac{i}{c(\theta)}		h[0](theta , alpha) = (exp(I*alpha*(Pi - theta)))/(1 + exp(- I*theta))-(I)/(c(theta))	Subscript[h, 0][\[Theta], \[Alpha]] == Divide[Exp[I*\[Alpha]*(Pi - \[Theta])],1 + Exp[- I*\[Theta]]]-Divide[I,c[\[Theta]]]	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11.E19	${\displaystyle{\displaystyle w_{j}(z)=e^{\lambda_{j}z}z^{\mu_{j}}\sum_{s=0}^{n-1}\frac{a_{s,j}}{z^{s}}+R_{n}^{(j)}(z)}}$ w_{j}(z) = e^{\lambda_{j}z}z^{\mu_{j}}\sum_{s=0}^{n-1}\frac{a_{s,j}}{z^{s}}+R_{n}^{(j)}(z)		w[j](z) = exp(lambda[j]*z)*(z)^(mu[j])* sum((a[s , j])/((z)^(s)), s = 0..n - 1)+ (R[n])^(j)(z)	Subscript[w, j][z] == Exp[Subscript[\[Lambda], j]*z]*(z)^(Subscript[\[Mu], j])* Sum[Divide[Subscript[a, s , j],(z)^(s)], {s, 0, n - 1}, GenerateConditions->None]+ (Subscript[R, n])^(j)[z]	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11.E26	${\displaystyle{\displaystyle e^{5}E_{1}\left(5\right)=0.17042\dots}}$ e^{5}\expintE@{5} = 0.17042\dots		exp(5)*Ei(5) = 0.17042	Exp[5]*ExpIntegralE[1, 5] == 0.17042	Failure	Failure	Skip - No test values generated	Successful [Tested: 1]
2.11#Ex4	${\displaystyle{\displaystyle\Delta^{0}=0.00768}}$ \Delta^{0} = 0.00768		(Delta)^(0) = 0.00768	\[CapitalDelta]^(0) == 0.00768	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11#Ex5	${\displaystyle{\displaystyle\Delta^{1}=0.00154}}$ \Delta^{1} = 0.00154		(Delta)^(1) = 0.00154	\[CapitalDelta]^(1) == 0.00154	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11#Ex6	${\displaystyle{\displaystyle\Delta^{2}=0.00214}}$ \Delta^{2} = 0.00214		(Delta)^(2) = 0.00214	\[CapitalDelta]^(2) == 0.00214	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11#Ex7	${\displaystyle{\displaystyle\Delta^{3}=0.00192}}$ \Delta^{3} = 0.00192		(Delta)^(3) = 0.00192	\[CapitalDelta]^(3) == 0.00192	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11#Ex8	${\displaystyle{\displaystyle\Delta^{4}=0.00280}}$ \Delta^{4} = 0.00280		(Delta)^(4) = 0.00280	\[CapitalDelta]^(4) == 0.00280	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11#Ex9	${\displaystyle{\displaystyle\Delta^{5}=0.00434}}$ \Delta^{5} = 0.00434		(Delta)^(5) = 0.00434	\[CapitalDelta]^(5) == 0.00434	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11.E28	${\displaystyle{\displaystyle 0.00384-0.00038+0.00027-0.00012+0.00009-0.00007=0.00363}}$ 0.00384-0.00038+0.00027-0.00012+0.00009-0.00007 = 0.00363		0.00384 - 0.00038 + 0.00027 - 0.00012 + 0.00009 - 0.00007 = 0.00363	0.00384 - 0.00038 + 0.00027 - 0.00012 + 0.00009 - 0.00007 == 0.00363	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11.E30	${\displaystyle{\displaystyle a_{n}=\frac{e^{-z/2}}{z^{n-\kappa}n!}\left(\mu^{2}-(\kappa-\tfrac{1}{2})^{2}\right)\*\left(\mu^{2}-(\kappa-\tfrac{3}{2})^{2}\right)\*\cdot\cdot\cdot\left(\mu^{2}-(\kappa-n+\tfrac{1}{2})^{2}\right)}}$ a_{n} = \frac{e^{-z/2}}{z^{n-\kappa}n!}\left(\mu^{2}-(\kappa-\tfrac{1}{2})^{2}\right)\*\left(\mu^{2}-(\kappa-\tfrac{3}{2})^{2}\right)\*\cdot\cdot\cdot\left(\mu^{2}-(\kappa-n+\tfrac{1}{2})^{2}\right)		a[n] = (exp(- z/2))/((z)^(n - kappa)* factorial(n))*((mu)^(2)-(kappa -(1)/(2))^(2))*((mu)^(2)-(kappa -(3)/(2))^(2))* * * *((mu)^(2)-(kappa - n +(1)/(2))^(2))	Subscript[a, n] == Divide[Exp[- z/2],(z)^(n - \[Kappa])* (n)!]*(\[Mu]^(2)-(\[Kappa]-Divide[1,2])^(2))*(\[Mu]^(2)-(\[Kappa]-Divide[3,2])^(2))* * * *(\[Mu]^(2)-(\[Kappa]- n +Divide[1,2])^(2))	Skipped - no semantic math	Skipped - no semantic math	-	-
2.11.E31	${\displaystyle{\displaystyle W_{2.3,0.5}\left(1.0\right)=-0.83299\;50268\;27526\;\cdots}}$ \WhittakerconfhyperW{2.3}{0.5}@{1.0} = -0.83299\;50268\;27526\;\cdots		WhittakerW(2.3, 0.5, 1.0) = - 0.832995026827526	WhittakerW[2.3, 0.5, 1.0] == - 0.832995026827526	Successful	Failure	-	Successful [Tested: 1]
2.11.E32	${\displaystyle{\displaystyle d_{n}=\frac{\sum_{j=0}^{n}(-1)^{j}\genfrac{(}{)}{0.0pt}{}{n}{j}(j+1)^{n-1}\frac{s_{j}}{a_{j+1}}}{\sum_{j=0}^{n}(-1)^{j}\genfrac{(}{)}{0.0pt}{}{n}{j}(j+1)^{n-1}\frac{1}{a_{j+1}}}}}$ d_{n} = \frac{\sum_{j=0}^{n}(-1)^{j}\binom{n}{j}(j+1)^{n-1}\frac{s_{j}}{a_{j+1}}}{\sum_{j=0}^{n}(-1)^{j}\binom{n}{j}(j+1)^{n-1}\frac{1}{a_{j+1}}}		d[n] = (sum((- 1)^(j)*binomial(n,j)*(j + 1)^(n - 1)*(s[j])/(a[j + 1]), j = 0..n))/(sum((- 1)^(j)*binomial(n,j)*(j + 1)^(n - 1)*(1)/(a[j + 1]), j = 0..n))	Subscript[d, n] == Divide[Sum[(- 1)^(j)*Binomial[n,j]*(j + 1)^(n - 1)*Divide[Subscript[s, j],Subscript[a, j + 1]], {j, 0, n}, GenerateConditions->None],Sum[(- 1)^(j)*Binomial[n,j]*(j + 1)^(n - 1)*Divide[1,Subscript[a, j + 1]], {j, 0, n}, GenerateConditions->None]]	Failure	Failure	Error	Skipped - Because timed out