10.20

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
10.20.E1	${\displaystyle{\displaystyle\left(\frac{\mathrm{d}\zeta}{\mathrm{d}z}\right)^{2}=\frac{1-z^{2}}{\zeta z^{2}}}}$ \left(\deriv{\zeta}{z}\right)^{2} = \frac{1-z^{2}}{\zeta z^{2}}		(diff(zeta, z))^(2) = (1 - (z)^(2))/(zeta*(z)^(2))	(D[\[Zeta], z])^(2) == Divide[1 - (z)^(2),\[Zeta]*(z)^(2)]	Failure	Failure	Failed [70 / 70] Result: .8660254030+.4999999994*I Test Values: {z = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I} Result: .4999999994-.8660254030*I Test Values: {z = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [70 / 70] Result: Complex[0.8660254037844386, 0.4999999999999999] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.4999999999999999, -0.8660254037844386] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
10.20.E2	${\displaystyle{\displaystyle\frac{2}{3}\zeta^{\frac{3}{2}}=\int_{z}^{1}\frac{\sqrt{1-t^{2}}}{t}\mathrm{d}t}}$ \frac{2}{3}\zeta^{\frac{3}{2}} = \int_{z}^{1}\frac{\sqrt{1-t^{2}}}{t}\diff{t}	${\displaystyle{\displaystyle 0<z,z\leq 1}}$	(2)/(3)*(zeta)^((3)/(2)) = int((sqrt(1 - (t)^(2)))/(t), t = z..1)	Divide[2,3]*\[Zeta]^(Divide[3,2]) == Integrate[Divide[Sqrt[1 - (t)^(2)],t], {t, z, 1}, GenerateConditions->None]	Error	Aborted	-	Skipped - Because timed out
10.20.E2	${\displaystyle{\displaystyle\int_{z}^{1}\frac{\sqrt{1-t^{2}}}{t}\mathrm{d}t=\ln\left(\frac{1+\sqrt{1-z^{2}}}{z}\right)-\sqrt{1-z^{2}}}}$ \int_{z}^{1}\frac{\sqrt{1-t^{2}}}{t}\diff{t} = \ln@{\frac{1+\sqrt{1-z^{2}}}{z}}-\sqrt{1-z^{2}}	${\displaystyle{\displaystyle 0<z,z\leq 1}}$	int((sqrt(1 - (t)^(2)))/(t), t = z..1) = ln((1 +sqrt(1 - (z)^(2)))/(z))-sqrt(1 - (z)^(2))	Integrate[Divide[Sqrt[1 - (t)^(2)],t], {t, z, 1}, GenerateConditions->None] == Log[Divide[1 +Sqrt[1 - (z)^(2)],z]]-Sqrt[1 - (z)^(2)]	Error	Aborted	-	Skipped - Because timed out
10.20.E3	${\displaystyle{\displaystyle\frac{2}{3}(-\zeta)^{\frac{3}{2}}=\int_{1}^{z}\frac{\sqrt{t^{2}-1}}{t}\mathrm{d}t}}$ \frac{2}{3}(-\zeta)^{\frac{3}{2}} = \int_{1}^{z}\frac{\sqrt{t^{2}-1}}{t}\diff{t}	${\displaystyle{\displaystyle 1\leq z,z<\infty}}$	(2)/(3)*(- zeta)^((3)/(2)) = int((sqrt((t)^(2)- 1))/(t), t = 1..z)	Divide[2,3]*(- \[Zeta])^(Divide[3,2]) == Integrate[Divide[Sqrt[(t)^(2)- 1],t], {t, 1, z}, GenerateConditions->None]	Failure	Aborted	Failed [20 / 20] Result: -.7483698391+.4714045210*I Test Values: {z = 3/2, zeta = 1/2*3^(1/2)+1/2*I} Result: -.2769653183-.6666666667*I Test Values: {z = 3/2, zeta = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [20 / 20] Result: Complex[-0.7483698389729962, 0.4714045207910317] Test Values: {Rule[z, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.27696531818196457, -0.6666666666666666] Test Values: {Rule[z, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
10.20.E3	${\displaystyle{\displaystyle\int_{1}^{z}\frac{\sqrt{t^{2}-1}}{t}\mathrm{d}t=\sqrt{z^{2}-1}-\operatorname{arcsec}z}}$ \int_{1}^{z}\frac{\sqrt{t^{2}-1}}{t}\diff{t} = \sqrt{z^{2}-1}-\asec@@{z}	${\displaystyle{\displaystyle 1\leq z,z<\infty}}$	int((sqrt((t)^(2)- 1))/(t), t = 1..z) = sqrt((z)^(2)- 1)- arcsec(z)	Integrate[Divide[Sqrt[(t)^(2)- 1],t], {t, 1, z}, GenerateConditions->None] == Sqrt[(z)^(2)- 1]- ArcSec[z]	Failure	Aborted	Successful [Tested: 2]	Successful [Tested: 2]
10.20#Ex1	${\displaystyle{\displaystyle A_{0}(0)=1}}$ A_{0}(0) = 1		A[0](0) = 1	Subscript[A, 0][0] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20#Ex2	${\displaystyle{\displaystyle A_{1}(0)=-\tfrac{1}{225}}}$ A_{1}(0) = -\tfrac{1}{225}		A[1](0) = -(1)/(225)	Subscript[A, 1][0] == -Divide[1,225]	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20#Ex3	${\displaystyle{\displaystyle A_{2}(0)=\tfrac{1\;51439}{2182\;95000}}}$ A_{2}(0) = \tfrac{1\;51439}{2182\;95000}		A[2](0) = (151439)/(218295000)	Subscript[A, 2][0] == Divide[151439,218295000]	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20#Ex4	${\displaystyle{\displaystyle A_{3}(0)=-\tfrac{8872\;78009}{250\;49351\;25000}}}$ A_{3}(0) = -\tfrac{8872\;78009}{250\;49351\;25000}		A[3](0) = -(887278009)/(2504935125000)	Subscript[A, 3][0] == -Divide[887278009,2504935125000]	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20#Ex5	${\displaystyle{\displaystyle B_{0}(0)=\tfrac{1}{70}2^{\frac{1}{3}}}}$ B_{0}(0) = \tfrac{1}{70}2^{\frac{1}{3}}		B[0](0) = (1)/(70)*(2)^((1)/(3))	Subscript[B, 0][0] == Divide[1,70]*(2)^(Divide[1,3])	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20#Ex6	${\displaystyle{\displaystyle B_{1}(0)=-\tfrac{1213}{10\;23750}2^{\frac{1}{3}}}}$ B_{1}(0) = -\tfrac{1213}{10\;23750}2^{\frac{1}{3}}		B[1](0) = -(1213)/(1023750)*(2)^((1)/(3))	Subscript[B, 1][0] == -Divide[1213,1023750]*(2)^(Divide[1,3])	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20#Ex7	${\displaystyle{\displaystyle B_{2}(0)=\tfrac{1\;65425\;37833}{3774\;32055\;00000}2^{\frac{1}{3}}}}$ B_{2}(0) = \tfrac{1\;65425\;37833}{3774\;32055\;00000}2^{\frac{1}{3}}		B[2](0) = (16542537833)/(37743205500000)*(2)^((1)/(3))	Subscript[B, 2][0] == Divide[16542537833,37743205500000]*(2)^(Divide[1,3])	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20#Ex8	${\displaystyle{\displaystyle B_{3}(0)=-\tfrac{959\;71711\;84603}{25\;47666\;37125\;00000}2^{\frac{1}{3}}}}$ B_{3}(0) = -\tfrac{959\;71711\;84603}{25\;47666\;37125\;00000}2^{\frac{1}{3}}		B[3](0) = -(9597171184603)/(25476663712500000)*(2)^((1)/(3))	Subscript[B, 3][0] == -Divide[9597171184603,25476663712500000]*(2)^(Divide[1,3])	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20.E15	${\displaystyle{\displaystyle\zeta=(\tfrac{3}{2})^{\frac{2}{3}}(\tau-i\pi)^{\frac{2}{3}}}}$ \zeta = (\tfrac{3}{2})^{\frac{2}{3}}(\tau- i\pi)^{\frac{2}{3}}	${\displaystyle{\displaystyle 0\leq\tau,\tau<\infty}}$	zeta = ((3)/(2))^((2)/(3))*(tau - I*Pi)^((2)/(3))	\[Zeta] == (Divide[3,2])^(Divide[2,3])*(\[Tau]- I*Pi)^(Divide[2,3])	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20.E16	${\displaystyle{\displaystyle\zeta=e^{-i\pi/3}\tau}}$ \zeta = e^{- i\pi/3}\tau	${\displaystyle{\displaystyle 0\leq\tau,\tau\leq(\tfrac{3}{2}\pi)^{\frac{2}{3}}}}$	zeta = exp(- I*Pi/3)*tau	\[Zeta] == Exp[- I*Pi/3]*\[Tau]	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20.E17	${\displaystyle{\displaystyle z=+(\tau\coth\tau-\tau^{2})^{\frac{1}{2}}+\mathrm{i}(\tau^{2}-\tau\tanh\tau)^{\frac{1}{2}}}}$ z = +(\tau\coth@@{\tau}-\tau^{2})^{\frac{1}{2}}+\iunit(\tau^{2}-\tau\tanh@@{\tau})^{\frac{1}{2}}	${\displaystyle{\displaystyle 0\leq\tau,\tau\leq\tau_{0}}}$	z = +(tau*coth(tau)- (tau)^(2))^((1)/(2))+ I*((tau)^(2)- tau*tanh(tau))^((1)/(2))	z == +(\[Tau]*Coth[\[Tau]]- \[Tau]^(2))^(Divide[1,2])+ I*(\[Tau]^(2)- \[Tau]*Tanh[\[Tau]])^(Divide[1,2])	Failure	Failure	Failed [21 / 21] Result: .8660254040-1.214547924*I Test Values: {tau = 3/2, z = 1/2*3^(1/2)+1/2*I} Result: -.5000000000-.8485225201*I Test Values: {tau = 3/2, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Skip - No test values generated
10.20.E17	${\displaystyle{\displaystyle z=-(\tau\coth\tau-\tau^{2})^{\frac{1}{2}}-\mathrm{i}(\tau^{2}-\tau\tanh\tau)^{\frac{1}{2}}}}$ z = -(\tau\coth@@{\tau}-\tau^{2})^{\frac{1}{2}}-\iunit(\tau^{2}-\tau\tanh@@{\tau})^{\frac{1}{2}}	${\displaystyle{\displaystyle 0\leq\tau,\tau\leq\tau_{0}}}$	z = -(tau*coth(tau)- (tau)^(2))^((1)/(2))- I*((tau)^(2)- tau*tanh(tau))^((1)/(2))	z == -(\[Tau]*Coth[\[Tau]]- \[Tau]^(2))^(Divide[1,2])- I*(\[Tau]^(2)- \[Tau]*Tanh[\[Tau]])^(Divide[1,2])	Failure	Failure	Failed [21 / 21] Result: .8660254040+2.214547924*I Test Values: {tau = 3/2, z = 1/2*3^(1/2)+1/2*I} Result: -.5000000000+2.580573328*I Test Values: {tau = 3/2, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Skip - No test values generated