4.37: Difference between revisions

Latest revision as of 11:10, 28 June 2021

DLMF	Formula	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
4.37.E1	${\displaystyle{\displaystyle\operatorname{Arcsinh}z=\int_{0}^{z}\frac{\mathrm{% d}t}{(1+t^{2})^{1/2}}}}$ `\Asinh@@{z} = \int_{0}^{z}\frac{\diff{t}}{(1+t^{2})^{1/2}}`	Error	ArcSinh[z] == Integrate[Divide[1,(1 + (t)^(2))^(1/2)], {t, 0, z}, GenerateConditions->None]	Missing Macro Error	Successful	-	Successful [Tested: 7]
4.37.E2	${\displaystyle{\displaystyle\operatorname{Arccosh}z=\int_{1}^{z}\frac{\mathrm{% d}t}{(t^{2}-1)^{1/2}}}}$ `\Acosh@@{z} = \int_{1}^{z}\frac{\diff{t}}{(t^{2}-1)^{1/2}}`	Error	ArcCosh[z] == Integrate[Divide[1,((t)^(2)- 1)^(1/2)], {t, 1, z}, GenerateConditions->None]	Missing Macro Error	Aborted	-	Skipped - Because timed out
4.37.E3	${\displaystyle{\displaystyle\operatorname{Arctanh}z=\int_{0}^{z}\frac{\mathrm{% d}t}{1-t^{2}}}}$ `\Atanh@@{z} = \int_{0}^{z}\frac{\diff{t}}{1-t^{2}}`	Error	ArcTanh[z] == Integrate[Divide[1,1 - (t)^(2)], {t, 0, z}, GenerateConditions->None]	Missing Macro Error	Successful	-	Successful [Tested: 1]
4.37.E4	${\displaystyle{\displaystyle\operatorname{Arccsch}z=\operatorname{Arcsinh}% \left(1/z\right)}}$ `\Acsch@@{z} = \Asinh@{1/z}`	Error	ArcCsch[z] == ArcSinh[1/z]	Missing Macro Error	Successful	-	Successful [Tested: 7]
4.37.E5	${\displaystyle{\displaystyle\operatorname{Arcsech}z=\operatorname{Arccosh}% \left(1/z\right)}}$ `\Asech@@{z} = \Acosh@{1/z}`	Error	ArcSech[z] == ArcCosh[1/z]	Missing Macro Error	Successful	-	Successful [Tested: 7]
4.37.E6	${\displaystyle{\displaystyle\operatorname{Arccoth}z=\operatorname{Arctanh}% \left(1/z\right)}}$ `\Acoth@@{z} = \Atanh@{1/z}`	Error	ArcCoth[z] == ArcTanh[1/z]	Missing Macro Error	Successful	-	Successful [Tested: 7]
4.37.E7	${\displaystyle{\displaystyle\operatorname{arccsch}z=\operatorname{arcsinh}% \left(1/z\right)}}$ `\acsch@@{z} = \asinh@{1/z}`	arccsch(z) = arcsinh(1/z)	ArcCsch[z] == ArcSinh[1/z]	Failure	Successful	Successful [Tested: 7]	Successful [Tested: 7]
4.37.E8	${\displaystyle{\displaystyle\operatorname{arcsech}z=\operatorname{arccosh}% \left(1/z\right)}}$ `\asech@@{z} = \acosh@{1/z}`	arcsech(z) = arccosh(1/z)	ArcSech[z] == ArcCosh[1/z]	Failure	Successful	Successful [Tested: 7]	Successful [Tested: 7]
4.37.E9	${\displaystyle{\displaystyle\operatorname{arccoth}z=\operatorname{arctanh}% \left(1/z\right)}}$ `\acoth@@{z} = \atanh@{1/z}`	arccoth(z) = arctanh(1/z)	ArcCoth[z] == ArcTanh[1/z]	Failure	Successful	Successful [Tested: 7]	Successful [Tested: 1]
4.37.E10	${\displaystyle{\displaystyle\operatorname{arcsinh}\left(-z\right)=-% \operatorname{arcsinh}z}}$ `\asinh@{-z} = -\asinh@@{z}`	arcsinh(- z) = - arcsinh(z)	ArcSinh[- z] == - ArcSinh[z]	Successful	Successful	-	Successful [Tested: 7]
4.37.E11	${\displaystyle{\displaystyle\operatorname{arccosh}\left(-z\right)=+\pi i+% \operatorname{arccosh}z}}$ `\acosh@{-z} = +\pi i+\acosh@@{z}`	arccosh(- z) = + Pi*I + arccosh(z)	ArcCosh[- z] == + Pi*I + ArcCosh[z]	Failure	Failure	Failed [3 / 7] Result: 0.-6.283185307I Test Values: {z = 1/23^(1/2)+1/2I, Im(z) = 1/2} Result: 0.-6.283185307I Test Values: {z = -1/2+1/2I3^(1/2), Im(z) = 1/2} Result: -2.094395103*I Test Values: {z = .5, Im(z) = 1/2}	Failed [1 / 1] Result: Complex[0.0, -6.283185307179586] Test Values: {Rule[z, Complex[0, Rational[1, 2]]]}
4.37.E11	${\displaystyle{\displaystyle\operatorname{arccosh}\left(-z\right)=-\pi i+% \operatorname{arccosh}z}}$ `\acosh@{-z} = -\pi i+\acosh@@{z}`	arccosh(- z) = - Pi*I + arccosh(z)	ArcCosh[- z] == - Pi*I + ArcCosh[z]	Failure	Failure	Failed [5 / 7] Result: 0.+6.283185307I Test Values: {z = 1/2-1/2I3^(1/2), Im(z) = 1/2} Result: 0.+6.283185307I Test Values: {z = -1/23^(1/2)-1/2I, Im(z) = 1/2} Result: 0.+6.283185308I Test Values: {z = 1.5, Im(z) = 1/2} Result: 4.188790205I Test Values: {z = .5, Im(z) = 1/2} ... skip entries to safe data	Successful [Tested: 1]
4.37.E12	${\displaystyle{\displaystyle\operatorname{arctanh}\left(-z\right)=-% \operatorname{arctanh}z}}$ `\atanh@{-z} = -\atanh@@{z}`	arctanh(- z) = - arctanh(z)	ArcTanh[- z] == - ArcTanh[z]	Successful	Successful	-	Successful [Tested: 1]
4.37.E13	${\displaystyle{\displaystyle\operatorname{arccsch}\left(-z\right)=-% \operatorname{arccsch}z}}$ `\acsch@{-z} = -\acsch@@{z}`	arccsch(- z) = - arccsch(z)	ArcCsch[- z] == - ArcCsch[z]	Successful	Successful	-	Successful [Tested: 7]
4.37.E14	${\displaystyle{\displaystyle\operatorname{arcsech}\left(-z\right)=-\pi i+% \operatorname{arcsech}z}}$ `\asech@{-z} = -\pi i+\asech@@{z}`	arcsech(- z) = - Pi*I + arcsech(z)	ArcSech[- z] == - Pi*I + ArcSech[z]	Failure	Failure	Failed [5 / 7] Result: 0.+6.283185307I Test Values: {z = 1/23^(1/2)+1/2I, Im(z) = 1/2} Result: 0.+6.283185307I Test Values: {z = -1/2+1/2I3^(1/2), Im(z) = 1/2} Result: 4.601047966I Test Values: {z = 1.5, Im(z) = 1/2} Result: 0.+6.283185308I Test Values: {z = .5, Im(z) = 1/2} ... skip entries to safe data	Failed [1 / 1] Result: Complex[0.0, 6.283185307179586] Test Values: {Rule[z, Complex[0, Rational[1, 2]]]}
4.37.E14	${\displaystyle{\displaystyle\operatorname{arcsech}\left(-z\right)=+\pi i+% \operatorname{arcsech}z}}$ `\asech@{-z} = +\pi i+\asech@@{z}`	arcsech(- z) = + Pi*I + arcsech(z)	ArcSech[- z] == + Pi*I + ArcSech[z]	Failure	Failure	Failed [4 / 7] Result: 0.-6.283185307I Test Values: {z = 1/2-1/2I3^(1/2), Im(z) = 1/2} Result: 0.-6.283185307I Test Values: {z = -1/23^(1/2)-1/2I, Im(z) = 1/2} Result: -1.682137342I Test Values: {z = 1.5, Im(z) = 1/2} Result: -2.094395103I Test Values: {z = 2, Im(z) = 1/2}	Successful [Tested: 1]
4.37.E15	${\displaystyle{\displaystyle\operatorname{arccoth}\left(-z\right)=-% \operatorname{arccoth}z}}$ `\acoth@{-z} = -\acoth@@{z}`	arccoth(- z) = - arccoth(z)	ArcCoth[- z] == - ArcCoth[z]	Failure	Successful	Failed [1 / 7] Result: 0.-3.141592654*I Test Values: {z = .5, z = 1/2}	Successful [Tested: 1]
4.37.E16	${\displaystyle{\displaystyle\operatorname{arcsinh}z=\ln\left((z^{2}+1)^{1/2}+z% \right)}}$ `\asinh@@{z} = \ln@{(z^{2}+1)^{1/2}+z}`	arcsinh(z) = ln(((z)^(2)+ 1)^(1/2)+ z)	ArcSinh[z] == Log[((z)^(2)+ 1)^(1/2)+ z]	Failure	Successful	Successful [Tested: 7]	Successful [Tested: 1]
4.37.E17	${\displaystyle{\displaystyle\operatorname{arcsinh}\left(iy\right)=\tfrac{1}{2}% \pi i+\ln\left((y^{2}-1)^{1/2}+y\right)}}$ `\asinh@{iy} = \tfrac{1}{2}\pi i+\ln@{(y^{2}-1)^{1/2}+y}`	arcsinh(Iy) = (1)/(2)Pi*I + ln(((y)^(2)- 1)^(1/2)+ y)	ArcSinh[Iy] == Divide[1,2]Pi*I + Log[((y)^(2)- 1)^(1/2)+ y]	Failure	Successful	Failed [4 / 6] Result: .7e-9-6.283185308I Test Values: {y = -1.5, y = 3/2} Result: -.1347500000e-10-4.188790205I Test Values: {y = -.5, y = 3/2} Result: -.1347500000e-10-2.094395102I Test Values: {y = .5, y = 3/2} Result: .2e-8-6.283185308I Test Values: {y = -2, y = 3/2}	Successful [Tested: 1]
4.37.E17	${\displaystyle{\displaystyle\operatorname{arcsinh}\left(iy\right)=\tfrac{1}{2}% \pi i-\ln\left((y^{2}-1)^{1/2}+y\right)}}$ `\asinh@{iy} = \tfrac{1}{2}\pi i-\ln@{(y^{2}-1)^{1/2}+y}`	arcsinh(Iy) = (1)/(2)Pi*I - ln(((y)^(2)- 1)^(1/2)+ y)	ArcSinh[Iy] == Divide[1,2]Pi*I - Log[((y)^(2)- 1)^(1/2)+ y]	Failure	Failure	Failed [4 / 6] Result: -1.924847301+0.I Test Values: {y = -1.5, y = 3/2} Result: 1.924847300+0.I Test Values: {y = 1.5, y = 3/2} Result: -2.633915796+0.I Test Values: {y = -2, y = 3/2} Result: 2.633915794+0.I Test Values: {y = 2, y = 3/2}	Failed [1 / 1] Result: Complex[1.9248473002384139, 0.0] Test Values: {Rule[y, Rational[3, 2]]}
4.37.E18	${\displaystyle{\displaystyle\operatorname{arcsinh}\left(iy\right)=-\tfrac{1}{2% }\pi i+\ln\left((y^{2}-1)^{1/2}-y\right)}}$ `\asinh@{iy} = -\tfrac{1}{2}\pi i+\ln@{(y^{2}-1)^{1/2}-y}`	arcsinh(Iy) = -(1)/(2)Pi*I + ln(((y)^(2)- 1)^(1/2)- y)	ArcSinh[Iy] == -Divide[1,2]Pi*I + Log[((y)^(2)- 1)^(1/2)- y]	Failure	Failure	Failed [4 / 6] Result: -1.924847300+0.I Test Values: {y = -1.5, y = -2} Result: 1.924847301+0.I Test Values: {y = 1.5, y = -2} Result: -2.633915794+0.I Test Values: {y = -2, y = -2} Result: 2.633915796+0.I Test Values: {y = 2, y = -2}	Failed [1 / 1] Result: Complex[-2.633915793849633, 0.0] Test Values: {Rule[y, -2]}
4.37.E18	${\displaystyle{\displaystyle\operatorname{arcsinh}\left(iy\right)=-\tfrac{1}{2% }\pi i-\ln\left((y^{2}-1)^{1/2}-y\right)}}$ `\asinh@{iy} = -\tfrac{1}{2}\pi i-\ln@{(y^{2}-1)^{1/2}-y}`	arcsinh(Iy) = -(1)/(2)Pi*I - ln(((y)^(2)- 1)^(1/2)- y)	ArcSinh[Iy] == -Divide[1,2]Pi*I - Log[((y)^(2)- 1)^(1/2)- y]	Failure	Failure	Failed [4 / 6] Result: -.7e-9+6.283185308I Test Values: {y = 1.5, y = -2} Result: .1347500000e-10+2.094395102I Test Values: {y = -.5, y = -2} Result: .1347500000e-10+4.188790205I Test Values: {y = .5, y = -2} Result: -.2e-8+6.283185308I Test Values: {y = 2, y = -2}	Successful [Tested: 1]
4.37.E19	${\displaystyle{\displaystyle\operatorname{arccosh}z=\ln\left(+(z^{2}-1)^{1/2}+% z\right)}}$ `\acosh@@{z} = \ln@{+(z^{2}-1)^{1/2}+z}`	arccosh(z) = ln(+((z)^(2)- 1)^(1/2)+ z)	ArcCosh[z] == Log[+((z)^(2)- 1)^(1/2)+ z]	Failure	Failure	Failed [2 / 7] Result: 1.662885893+3.891061519I Test Values: {z = -1/2+1/2I3^(1/2), z = 3/2} Result: 1.316957897-4.712388980I Test Values: {z = -1/23^(1/2)-1/2I, z = 3/2}	Successful [Tested: 1]
4.37.E19	${\displaystyle{\displaystyle\operatorname{arccosh}z=\ln\left(-(z^{2}-1)^{1/2}+% z\right)}}$ `\acosh@@{z} = \ln@{-(z^{2}-1)^{1/2}+z}`	arccosh(z) = ln(-((z)^(2)- 1)^(1/2)+ z)	ArcCosh[z] == Log[-((z)^(2)- 1)^(1/2)+ z]	Failure	Failure	Failed [5 / 7] Result: 1.316957897+1.570796326I Test Values: {z = 1/23^(1/2)+1/2I, z = 3/2} Result: 1.662885893-2.392123788I Test Values: {z = 1/2-1/2I3^(1/2), z = 3/2} Result: 1.924847301 Test Values: {z = 1.5, z = 3/2} Result: -.1347500000e-10+2.094395102*I Test Values: {z = .5, z = 3/2} ... skip entries to safe data	Failed [1 / 1] Result: 1.9248473002384139 Test Values: {Rule[z, Rational[3, 2]]}
4.37.E20	${\displaystyle{\displaystyle\operatorname{arccosh}\left(\mathrm{i}y\right)=+% \tfrac{1}{2}\pi\mathrm{i}+\ln\left((y^{2}+1)^{1/2}+y\right)}}$ `\acosh@{\iunit y} = +\tfrac{1}{2}\pi\iunit+\ln@{(y^{2}+1)^{1/2}+ y}`	arccosh(Iy) = +(1)/(2)Pi*I + ln(((y)^(2)+ 1)^(1/2)+ y)	ArcCosh[Iy] == +Divide[1,2]Pi*I + Log[((y)^(2)+ 1)^(1/2)+ y]	Failure	Failure	Failed [3 / 6] Result: 2.389526433-3.141592654I Test Values: {y = -1.5, y = 1/2} Result: .9624236498-3.141592654I Test Values: {y = -.5, y = 1/2} Result: 2.887270952-3.141592654*I Test Values: {y = -2, y = 1/2}	Successful [Tested: 1]
4.37.E20	${\displaystyle{\displaystyle\operatorname{arccosh}\left(\mathrm{i}y\right)=-% \tfrac{1}{2}\pi\mathrm{i}+\ln\left((y^{2}+1)^{1/2}-y\right)}}$ `\acosh@{\iunit y} = -\tfrac{1}{2}\pi\iunit+\ln@{(y^{2}+1)^{1/2}- y}`	arccosh(Iy) = -(1)/(2)Pi*I + ln(((y)^(2)+ 1)^(1/2)- y)	ArcCosh[Iy] == -Divide[1,2]Pi*I + Log[((y)^(2)+ 1)^(1/2)- y]	Failure	Failure	Failed [3 / 6] Result: 2.389526433+3.141592654I Test Values: {y = 1.5, y = 1/2} Result: .9624236498+3.141592654I Test Values: {y = .5, y = 1/2} Result: 2.887270952+3.141592654*I Test Values: {y = 2, y = 1/2}	Failed [1 / 1] Result: Complex[0.9624236501192068, 3.141592653589793] Test Values: {Rule[y, Rational[1, 2]]}
4.37.E21	${\displaystyle{\displaystyle\operatorname{arccosh}z=2\ln\left(\left(\frac{z+1}% {2}\right)^{1/2}+\left(\frac{z-1}{2}\right)^{1/2}\right)}}$ `\acosh@@{z} = 2\ln@{\left(\frac{z+1}{2}\right)^{1/2}+\left(\frac{z-1}{2}\right)^{1/2}}`	arccosh(z) = 2*ln(((z + 1)/(2))^(1/2)+((z - 1)/(2))^(1/2))	ArcCosh[z] == 2*Log[(Divide[z + 1,2])^(1/2)+(Divide[z - 1,2])^(1/2)]	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 1]
4.37.E22	${\displaystyle{\displaystyle\operatorname{arccosh}x=+\ln\left(i(1-x^{2})^{1/2}% +x\right)}}$ `\acosh@@{x} = +\ln@{i(1-x^{2})^{1/2}+x}`	arccosh(x) = + ln(I*(1 - (x)^(2))^(1/2)+ x)	ArcCosh[x] == + Log[I*(1 - (x)^(2))^(1/2)+ x]	Failure	Failure	Failed [2 / 3] Result: 1.924847301 Test Values: {x = 1.5, x = 1/2} Result: 2.633915796 Test Values: {x = 2, x = 1/2}	Successful [Tested: 1]
4.37.E22	${\displaystyle{\displaystyle\operatorname{arccosh}x=-\ln\left(i(1-x^{2})^{1/2}% +x\right)}}$ `\acosh@@{x} = -\ln@{i(1-x^{2})^{1/2}+x}`	arccosh(x) = - ln(I*(1 - (x)^(2))^(1/2)+ x)	ArcCosh[x] == - Log[I*(1 - (x)^(2))^(1/2)+ x]	Failure	Failure	Failed [1 / 3] Result: .1347500000e-10+2.094395102*I Test Values: {x = .5, x = 1/2}	Failed [1 / 1] Result: Complex[0.0, 2.0943951023931953] Test Values: {Rule[x, Rational[1, 2]]}
4.37.E23	${\displaystyle{\displaystyle\operatorname{arccosh}x=+\pi i+\ln\left((x^{2}-1)^% {1/2}-x\right)}}$ `\acosh@@{x} = +\pi i+\ln@{(x^{2}-1)^{1/2}-x}`	arccosh(x) = + Pi*I + ln(((x)^(2)- 1)^(1/2)- x)	ArcCosh[x] == + Pi*I + Log[((x)^(2)- 1)^(1/2)- x]	Failure	Failure	Failed [3 / 3] Result: 1.924847301-6.283185308I Test Values: {x = 1.5, x = -2} Result: -.1347500000e-10-4.188790205I Test Values: {x = .5, x = -2} Result: 2.633915796-6.283185308*I Test Values: {x = 2, x = -2}	Successful [Tested: 1]
4.37.E23	${\displaystyle{\displaystyle\operatorname{arccosh}x=-\pi i+\ln\left((x^{2}-1)^% {1/2}-x\right)}}$ `\acosh@@{x} = -\pi i+\ln@{(x^{2}-1)^{1/2}-x}`	arccosh(x) = - Pi*I + ln(((x)^(2)- 1)^(1/2)- x)	ArcCosh[x] == - Pi*I + Log[((x)^(2)- 1)^(1/2)- x]	Failure	Failure	Failed [3 / 3] Result: 1.924847301+0.I Test Values: {x = 1.5, x = -2} Result: -.1347500000e-10+2.094395103I Test Values: {x = .5, x = -2} Result: 2.633915796+0.*I Test Values: {x = 2, x = -2}	Failed [1 / 1] Result: Complex[0.0, 6.283185307179586] Test Values: {Rule[x, -2]}
4.37.E24	${\displaystyle{\displaystyle\operatorname{arctanh}z=\tfrac{1}{2}\ln\left(\frac% {1+z}{1-z}\right)}}$ `\atanh@@{z} = \tfrac{1}{2}\ln@{\frac{1+z}{1-z}}`	arctanh(z) = (1)/(2)*ln((1 + z)/(1 - z))	ArcTanh[z] == Divide[1,2]*Log[Divide[1 + z,1 - z]]	Failure	Failure	Failed [2 / 7] Result: .2e-9-3.141592654I Test Values: {z = 1.5, z = 1/2} Result: -.2e-9-3.141592654I Test Values: {z = 2, z = 1/2}	Successful [Tested: 1]
4.37.E25	${\displaystyle{\displaystyle\operatorname{arctanh}x=+\tfrac{1}{2}\pi i+\tfrac{% 1}{2}\ln\left(\frac{x+1}{x-1}\right)}}$ `\atanh@@{x} = +\tfrac{1}{2}\pi i+\tfrac{1}{2}\ln@{\frac{x+1}{x-1}}`	arctanh(x) = +(1)/(2)PiI +(1)/(2)*ln((x + 1)/(x - 1))	ArcTanh[x] == +Divide[1,2]PiI +Divide[1,2]*Log[Divide[x + 1,x - 1]]	Failure	Failure	Failed [3 / 3] Result: .2e-9-3.141592654I Test Values: {x = 1.5, x = -3/2} Result: -.2e-9-3.141592654I Test Values: {x = .5, x = -3/2} Result: -.2e-9-3.141592654*I Test Values: {x = 2, x = -3/2}	Successful [Tested: 1]
4.37.E25	${\displaystyle{\displaystyle\operatorname{arctanh}x=-\tfrac{1}{2}\pi i+\tfrac{% 1}{2}\ln\left(\frac{x+1}{x-1}\right)}}$ `\atanh@@{x} = -\tfrac{1}{2}\pi i+\tfrac{1}{2}\ln@{\frac{x+1}{x-1}}`	arctanh(x) = -(1)/(2)PiI +(1)/(2)*ln((x + 1)/(x - 1))	ArcTanh[x] == -Divide[1,2]PiI +Divide[1,2]*Log[Divide[x + 1,x - 1]]	Failure	Failure	Successful [Tested: 3]	Failed [1 / 1] Result: Complex[-1.1102230246251565*^-16, 3.141592653589793] Test Values: {Rule[x, Rational[-3, 2]]}
4.37.E26	${\displaystyle{\displaystyle z=\sinh w}}$ `z = \sinh@@{w}`	z = sinh(w)	z == Sinh[w]	Failure	Failure	Failed [70 / 70] Result: .73886869e-2-.1707313589I Test Values: {w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -1.358636717+.1952940451I Test Values: {w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} Result: -.3586367171-1.536756763I Test Values: {w = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)} Result: -1.724662121-1.170731359I Test Values: {w = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I} ... skip entries to safe data	Failed [70 / 70] Result: Complex[0.007388686967293889, -0.17073135880721174] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.3586367168171445, 0.19529404497722702] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
4.37.E27	${\displaystyle{\displaystyle z=\cosh w}}$ `z = \cosh@@{w}`	z = cosh(w)	z == Cosh[w]	Failure	Failure	Failed [70 / 70] Result: -.3617401130+.309246236e-1I Test Values: {w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -1.727765517+.3969500276I Test Values: {w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} Result: -.7277655170-1.335100780I Test Values: {w = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)} Result: -2.093790921-.9690753764I Test Values: {w = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I} ... skip entries to safe data	Failed [70 / 70] Result: Complex[-0.3617401130796717, 0.030924623731496126] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.7277655168641102, 0.3969500275159349] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
4.37.E28	${\displaystyle{\displaystyle z=\tanh w}}$ `z = \tanh@@{w}`	z = tanh(w)	z == Tanh[w]	Failure	Failure	Failed [70 / 70] Result: .736226475e-1+.2564398629I Test Values: {w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -1.292402756+.6224652669I Test Values: {w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} Result: -.2924027565-1.109585541I Test Values: {w = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)} Result: -1.658428160-.7435601371I Test Values: {w = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I} ... skip entries to safe data	Failed [70 / 70] Result: Complex[0.07362264736640245, 0.25643986284286624] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.292402756418036, 0.622465266627305] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
4.37.E29	${\displaystyle{\displaystyle w=\operatorname{Arcsinh}z}}$ `w = \Asinh@@{z}`	Error	w == ArcSinh[z]	Missing Macro Error	Failure	-	Failed [70 / 70] Result: Complex[0.03458245825512818, 0.12526556729125993] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.524504352246847, -0.28539816339744856] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
4.37.E29	${\displaystyle{\displaystyle\operatorname{Arcsinh}z=(-1)^{k}\operatorname{% arcsinh}z+k\pi i}}$ `\Asinh@@{z} = (-1)^{k}\asinh@@{z}+k\pi i`	Error	ArcSinh[z] == (- 1)^(k)* ArcSinh[z]+ kPiI	Missing Macro Error	Failure	-	Failed [21 / 21] Result: Complex[1.662885891058621, -2.392123788172313] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.0, -6.283185307179586] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
4.37.E30	${\displaystyle{\displaystyle w=\operatorname{Arccosh}z}}$ `w = \Acosh@@{z}`	Error	w == ArcCosh[z]	Missing Macro Error	Failure	-	Failed [70 / 70] Result: Complex[0.20754645532203042, -0.28539816339744833] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.03458245825512796, -1.4455307595036366] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
4.37.E30	${\displaystyle{\displaystyle\operatorname{Arccosh}z=+\operatorname{arccosh}z+2% k\pi i}}$ `\Acosh@@{z} = +\acosh@@{z}+2k\pi i`	Error	ArcCosh[z] == + ArcCosh[z]+ 2kPi*I	Missing Macro Error	Failure	-	Failed [21 / 21] Result: Complex[0.0, -6.283185307179586] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.0, -12.566370614359172] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
4.37.E30	${\displaystyle{\displaystyle\operatorname{Arccosh}z=-\operatorname{arccosh}z+2% k\pi i}}$ `\Acosh@@{z} = -\acosh@@{z}+2k\pi i`	Error	ArcCosh[z] == - ArcCosh[z]+ 2kPi*I	Missing Macro Error	Failure	-	Failed [21 / 21] Result: Complex[1.3169578969248166, -4.71238898038469] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.3169578969248166, -10.995574287564276] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
4.37.E31	${\displaystyle{\displaystyle w=\operatorname{Arctanh}z}}$ `w = \Atanh@@{z}`	Error	w == ArcTanh[z]	Missing Macro Error	Failure	-	Failed [10 / 10] Result: Complex[0.3167192594503839, 0.49999999999999994] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Rational[1, 2]]} Result: Complex[-1.0493061443340546, 0.8660254037844387] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[z, Rational[1, 2]]} ... skip entries to safe data
4.37.E31	${\displaystyle{\displaystyle\operatorname{Arctanh}z=\operatorname{arctanh}z+k% \pi i}}$ `\Atanh@@{z} = \atanh@@{z}+k\pi i`	Error	ArcTanh[z] == ArcTanh[z]+ kPiI	Missing Macro Error	Failure	-	Failed [3 / 3] Result: Complex[0.0, -3.141592653589793] Test Values: {Rule[k, 1], Rule[z, Rational[1, 2]]} Result: Complex[0.0, -6.283185307179586] Test Values: {Rule[k, 2], Rule[z, Rational[1, 2]]} ... skip entries to safe data

@@ Line 14: / Line 14: @@
 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
 |-
-| [https://dlmf.nist.gov/4.37.E1 4.37.E1] || [[Item:Q1920|<math>\Asinh@@{z} = \int_{0}^{z}\frac{\diff{t}}{(1+t^{2})^{1/2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Asinh@@{z} = \int_{0}^{z}\frac{\diff{t}}{(1+t^{2})^{1/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[z] == Integrate[Divide[1,(1 + (t)^(2))^(1/2)], {t, 0, z}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.37.E1 4.37.E1] || <math qid="Q1920">\Asinh@@{z} = \int_{0}^{z}\frac{\diff{t}}{(1+t^{2})^{1/2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Asinh@@{z} = \int_{0}^{z}\frac{\diff{t}}{(1+t^{2})^{1/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[z] == Integrate[Divide[1,(1 + (t)^(2))^(1/2)], {t, 0, z}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.37.E2 4.37.E2] || [[Item:Q1921|<math>\Acosh@@{z} = \int_{1}^{z}\frac{\diff{t}}{(t^{2}-1)^{1/2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acosh@@{z} = \int_{1}^{z}\frac{\diff{t}}{(t^{2}-1)^{1/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[z] == Integrate[Divide[1,((t)^(2)- 1)^(1/2)], {t, 1, z}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/4.37.E2 4.37.E2] || <math qid="Q1921">\Acosh@@{z} = \int_{1}^{z}\frac{\diff{t}}{(t^{2}-1)^{1/2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acosh@@{z} = \int_{1}^{z}\frac{\diff{t}}{(t^{2}-1)^{1/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[z] == Integrate[Divide[1,((t)^(2)- 1)^(1/2)], {t, 1, z}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/4.37.E3 4.37.E3] || [[Item:Q1922|<math>\Atanh@@{z} = \int_{0}^{z}\frac{\diff{t}}{1-t^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Atanh@@{z} = \int_{0}^{z}\frac{\diff{t}}{1-t^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTanh[z] == Integrate[Divide[1,1 - (t)^(2)], {t, 0, z}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 1]
+| [https://dlmf.nist.gov/4.37.E3 4.37.E3] || <math qid="Q1922">\Atanh@@{z} = \int_{0}^{z}\frac{\diff{t}}{1-t^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Atanh@@{z} = \int_{0}^{z}\frac{\diff{t}}{1-t^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTanh[z] == Integrate[Divide[1,1 - (t)^(2)], {t, 0, z}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.37.E4 4.37.E4] || [[Item:Q1923|<math>\Acsch@@{z} = \Asinh@{1/z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acsch@@{z} = \Asinh@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCsch[z] == ArcSinh[1/z]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.37.E4 4.37.E4] || <math qid="Q1923">\Acsch@@{z} = \Asinh@{1/z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acsch@@{z} = \Asinh@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCsch[z] == ArcSinh[1/z]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.37.E5 4.37.E5] || [[Item:Q1924|<math>\Asech@@{z} = \Acosh@{1/z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Asech@@{z} = \Acosh@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSech[z] == ArcCosh[1/z]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.37.E5 4.37.E5] || <math qid="Q1924">\Asech@@{z} = \Acosh@{1/z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Asech@@{z} = \Acosh@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSech[z] == ArcCosh[1/z]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.37.E6 4.37.E6] || [[Item:Q1925|<math>\Acoth@@{z} = \Atanh@{1/z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acoth@@{z} = \Atanh@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCoth[z] == ArcTanh[1/z]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.37.E6 4.37.E6] || <math qid="Q1925">\Acoth@@{z} = \Atanh@{1/z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acoth@@{z} = \Atanh@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCoth[z] == ArcTanh[1/z]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.37.E7 4.37.E7] || [[Item:Q1926|<math>\acsch@@{z} = \asinh@{1/z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acsch@@{z} = \asinh@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccsch(z) = arcsinh(1/z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCsch[z] == ArcSinh[1/z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.37.E7 4.37.E7] || <math qid="Q1926">\acsch@@{z} = \asinh@{1/z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acsch@@{z} = \asinh@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccsch(z) = arcsinh(1/z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCsch[z] == ArcSinh[1/z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.37.E8 4.37.E8] || [[Item:Q1927|<math>\asech@@{z} = \acosh@{1/z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asech@@{z} = \acosh@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsech(z) = arccosh(1/z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSech[z] == ArcCosh[1/z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.37.E8 4.37.E8] || <math qid="Q1927">\asech@@{z} = \acosh@{1/z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asech@@{z} = \acosh@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsech(z) = arccosh(1/z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSech[z] == ArcCosh[1/z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.37.E9 4.37.E9] || [[Item:Q1928|<math>\acoth@@{z} = \atanh@{1/z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acoth@@{z} = \atanh@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccoth(z) = arctanh(1/z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCoth[z] == ArcTanh[1/z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 1]
+| [https://dlmf.nist.gov/4.37.E9 4.37.E9] || <math qid="Q1928">\acoth@@{z} = \atanh@{1/z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acoth@@{z} = \atanh@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccoth(z) = arctanh(1/z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCoth[z] == ArcTanh[1/z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.37.E10 4.37.E10] || [[Item:Q1929|<math>\asinh@{-z} = -\asinh@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asinh@{-z} = -\asinh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsinh(- z) = - arcsinh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[- z] == - ArcSinh[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.37.E10 4.37.E10] || <math qid="Q1929">\asinh@{-z} = -\asinh@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asinh@{-z} = -\asinh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsinh(- z) = - arcsinh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[- z] == - ArcSinh[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.37.E11 4.37.E11] || [[Item:Q1930|<math>\acosh@{-z} = +\pi i+\acosh@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@{-z} = +\pi i+\acosh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(- z) = + Pi*I + arccosh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[- z] == + Pi*I + ArcCosh[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0.-6.283185307*I
+| [https://dlmf.nist.gov/4.37.E11 4.37.E11] || <math qid="Q1930">\acosh@{-z} = +\pi i+\acosh@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@{-z} = +\pi i+\acosh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(- z) = + Pi*I + arccosh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[- z] == + Pi*I + ArcCosh[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0.-6.283185307*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, Im(z) = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0.-6.283185307*I
 Test Values: {z = -1/2+1/2*I*3^(1/2), Im(z) = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.094395103*I
@@ Line 40: / Line 40: @@
 Test Values: {Rule[z, Complex[0, Rational[1, 2]]]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E11 4.37.E11] || [[Item:Q1930|<math>\acosh@{-z} = -\pi i+\acosh@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@{-z} = -\pi i+\acosh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(- z) = - Pi*I + arccosh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[- z] == - Pi*I + ArcCosh[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [5 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0.+6.283185307*I
+| [https://dlmf.nist.gov/4.37.E11 4.37.E11] || <math qid="Q1930">\acosh@{-z} = -\pi i+\acosh@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@{-z} = -\pi i+\acosh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(- z) = - Pi*I + arccosh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[- z] == - Pi*I + ArcCosh[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [5 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0.+6.283185307*I
 Test Values: {z = 1/2-1/2*I*3^(1/2), Im(z) = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0.+6.283185307*I
 Test Values: {z = -1/2*3^(1/2)-1/2*I, Im(z) = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0.+6.283185308*I
@@ Line 46: / Line 46: @@
 Test Values: {z = .5, Im(z) = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.37.E12 4.37.E12] || [[Item:Q1931|<math>\atanh@{-z} = -\atanh@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atanh@{-z} = -\atanh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctanh(- z) = - arctanh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTanh[- z] == - ArcTanh[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
+| [https://dlmf.nist.gov/4.37.E12 4.37.E12] || <math qid="Q1931">\atanh@{-z} = -\atanh@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atanh@{-z} = -\atanh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctanh(- z) = - arctanh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTanh[- z] == - ArcTanh[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.37.E13 4.37.E13] || [[Item:Q1932|<math>\acsch@{-z} = -\acsch@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acsch@{-z} = -\acsch@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccsch(- z) = - arccsch(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCsch[- z] == - ArcCsch[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.37.E13 4.37.E13] || <math qid="Q1932">\acsch@{-z} = -\acsch@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acsch@{-z} = -\acsch@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccsch(- z) = - arccsch(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCsch[- z] == - ArcCsch[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.37.E14 4.37.E14] || [[Item:Q1933|<math>\asech@{-z} = -\pi i+\asech@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asech@{-z} = -\pi i+\asech@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsech(- z) = - Pi*I + arcsech(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSech[- z] == - Pi*I + ArcSech[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [5 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0.+6.283185307*I
+| [https://dlmf.nist.gov/4.37.E14 4.37.E14] || <math qid="Q1933">\asech@{-z} = -\pi i+\asech@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asech@{-z} = -\pi i+\asech@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsech(- z) = - Pi*I + arcsech(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSech[- z] == - Pi*I + ArcSech[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [5 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0.+6.283185307*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, Im(z) = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0.+6.283185307*I
 Test Values: {z = -1/2+1/2*I*3^(1/2), Im(z) = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 4.601047966*I
@@ Line 57: / Line 57: @@
 Test Values: {Rule[z, Complex[0, Rational[1, 2]]]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E14 4.37.E14] || [[Item:Q1933|<math>\asech@{-z} = +\pi i+\asech@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asech@{-z} = +\pi i+\asech@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsech(- z) = + Pi*I + arcsech(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSech[- z] == + Pi*I + ArcSech[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0.-6.283185307*I
+| [https://dlmf.nist.gov/4.37.E14 4.37.E14] || <math qid="Q1933">\asech@{-z} = +\pi i+\asech@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asech@{-z} = +\pi i+\asech@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsech(- z) = + Pi*I + arcsech(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSech[- z] == + Pi*I + ArcSech[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0.-6.283185307*I
 Test Values: {z = 1/2-1/2*I*3^(1/2), Im(z) = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0.-6.283185307*I
 Test Values: {z = -1/2*3^(1/2)-1/2*I, Im(z) = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.682137342*I
@@ Line 63: / Line 63: @@
 Test Values: {z = 2, Im(z) = 1/2}</syntaxhighlight><br></div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.37.E15 4.37.E15] || [[Item:Q1934|<math>\acoth@{-z} = -\acoth@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acoth@{-z} = -\acoth@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccoth(- z) = - arccoth(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCoth[- z] == - ArcCoth[z]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0.-3.141592654*I
+| [https://dlmf.nist.gov/4.37.E15 4.37.E15] || <math qid="Q1934">\acoth@{-z} = -\acoth@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acoth@{-z} = -\acoth@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccoth(- z) = - arccoth(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCoth[- z] == - ArcCoth[z]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0.-3.141592654*I
 Test Values: {z = .5, z = 1/2}</syntaxhighlight><br></div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.37.E16 4.37.E16] || [[Item:Q1935|<math>\asinh@@{z} = \ln@{(z^{2}+1)^{1/2}+z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asinh@@{z} = \ln@{(z^{2}+1)^{1/2}+z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsinh(z) = ln(((z)^(2)+ 1)^(1/2)+ z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[z] == Log[((z)^(2)+ 1)^(1/2)+ z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 1]
+| [https://dlmf.nist.gov/4.37.E16 4.37.E16] || <math qid="Q1935">\asinh@@{z} = \ln@{(z^{2}+1)^{1/2}+z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asinh@@{z} = \ln@{(z^{2}+1)^{1/2}+z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsinh(z) = ln(((z)^(2)+ 1)^(1/2)+ z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[z] == Log[((z)^(2)+ 1)^(1/2)+ z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.37.E17 4.37.E17] || [[Item:Q1936|<math>\asinh@{iy} = \tfrac{1}{2}\pi i+\ln@{(y^{2}-1)^{1/2}+y}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asinh@{iy} = \tfrac{1}{2}\pi i+\ln@{(y^{2}-1)^{1/2}+y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsinh(I*y) = (1)/(2)*Pi*I + ln(((y)^(2)- 1)^(1/2)+ y)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[I*y] == Divide[1,2]*Pi*I + Log[((y)^(2)- 1)^(1/2)+ y]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7e-9-6.283185308*I
+| [https://dlmf.nist.gov/4.37.E17 4.37.E17] || <math qid="Q1936">\asinh@{iy} = \tfrac{1}{2}\pi i+\ln@{(y^{2}-1)^{1/2}+y}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asinh@{iy} = \tfrac{1}{2}\pi i+\ln@{(y^{2}-1)^{1/2}+y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsinh(I*y) = (1)/(2)*Pi*I + ln(((y)^(2)- 1)^(1/2)+ y)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[I*y] == Divide[1,2]*Pi*I + Log[((y)^(2)- 1)^(1/2)+ y]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7e-9-6.283185308*I
 Test Values: {y = -1.5, y = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1347500000e-10-4.188790205*I
 Test Values: {y = -.5, y = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1347500000e-10-2.094395102*I
@@ Line 74: / Line 74: @@
 Test Values: {y = -2, y = 3/2}</syntaxhighlight><br></div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.37.E17 4.37.E17] || [[Item:Q1936|<math>\asinh@{iy} = \tfrac{1}{2}\pi i-\ln@{(y^{2}-1)^{1/2}+y}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asinh@{iy} = \tfrac{1}{2}\pi i-\ln@{(y^{2}-1)^{1/2}+y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsinh(I*y) = (1)/(2)*Pi*I - ln(((y)^(2)- 1)^(1/2)+ y)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[I*y] == Divide[1,2]*Pi*I - Log[((y)^(2)- 1)^(1/2)+ y]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.924847301+0.*I
+| [https://dlmf.nist.gov/4.37.E17 4.37.E17] || <math qid="Q1936">\asinh@{iy} = \tfrac{1}{2}\pi i-\ln@{(y^{2}-1)^{1/2}+y}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asinh@{iy} = \tfrac{1}{2}\pi i-\ln@{(y^{2}-1)^{1/2}+y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsinh(I*y) = (1)/(2)*Pi*I - ln(((y)^(2)- 1)^(1/2)+ y)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[I*y] == Divide[1,2]*Pi*I - Log[((y)^(2)- 1)^(1/2)+ y]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.924847301+0.*I
 Test Values: {y = -1.5, y = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.924847300+0.*I
 Test Values: {y = 1.5, y = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.633915796+0.*I
@@ Line 81: / Line 81: @@
 Test Values: {Rule[y, Rational[3, 2]]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E18 4.37.E18] || [[Item:Q1937|<math>\asinh@{iy} = -\tfrac{1}{2}\pi i+\ln@{(y^{2}-1)^{1/2}-y}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asinh@{iy} = -\tfrac{1}{2}\pi i+\ln@{(y^{2}-1)^{1/2}-y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsinh(I*y) = -(1)/(2)*Pi*I + ln(((y)^(2)- 1)^(1/2)- y)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[I*y] == -Divide[1,2]*Pi*I + Log[((y)^(2)- 1)^(1/2)- y]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.924847300+0.*I
+| [https://dlmf.nist.gov/4.37.E18 4.37.E18] || <math qid="Q1937">\asinh@{iy} = -\tfrac{1}{2}\pi i+\ln@{(y^{2}-1)^{1/2}-y}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asinh@{iy} = -\tfrac{1}{2}\pi i+\ln@{(y^{2}-1)^{1/2}-y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsinh(I*y) = -(1)/(2)*Pi*I + ln(((y)^(2)- 1)^(1/2)- y)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[I*y] == -Divide[1,2]*Pi*I + Log[((y)^(2)- 1)^(1/2)- y]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.924847300+0.*I
 Test Values: {y = -1.5, y = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.924847301+0.*I
 Test Values: {y = 1.5, y = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.633915794+0.*I
@@ Line 88: / Line 88: @@
 Test Values: {Rule[y, -2]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E18 4.37.E18] || [[Item:Q1937|<math>\asinh@{iy} = -\tfrac{1}{2}\pi i-\ln@{(y^{2}-1)^{1/2}-y}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asinh@{iy} = -\tfrac{1}{2}\pi i-\ln@{(y^{2}-1)^{1/2}-y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsinh(I*y) = -(1)/(2)*Pi*I - ln(((y)^(2)- 1)^(1/2)- y)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[I*y] == -Divide[1,2]*Pi*I - Log[((y)^(2)- 1)^(1/2)- y]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.7e-9+6.283185308*I
+| [https://dlmf.nist.gov/4.37.E18 4.37.E18] || <math qid="Q1937">\asinh@{iy} = -\tfrac{1}{2}\pi i-\ln@{(y^{2}-1)^{1/2}-y}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asinh@{iy} = -\tfrac{1}{2}\pi i-\ln@{(y^{2}-1)^{1/2}-y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsinh(I*y) = -(1)/(2)*Pi*I - ln(((y)^(2)- 1)^(1/2)- y)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[I*y] == -Divide[1,2]*Pi*I - Log[((y)^(2)- 1)^(1/2)- y]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.7e-9+6.283185308*I
 Test Values: {y = 1.5, y = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1347500000e-10+2.094395102*I
 Test Values: {y = -.5, y = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1347500000e-10+4.188790205*I
@@ Line 94: / Line 94: @@
 Test Values: {y = 2, y = -2}</syntaxhighlight><br></div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.37.E19 4.37.E19] || [[Item:Q1938|<math>\acosh@@{z} = \ln@{+(z^{2}-1)^{1/2}+z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@@{z} = \ln@{+(z^{2}-1)^{1/2}+z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(z) = ln(+((z)^(2)- 1)^(1/2)+ z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[z] == Log[+((z)^(2)- 1)^(1/2)+ z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.662885893+3.891061519*I
+| [https://dlmf.nist.gov/4.37.E19 4.37.E19] || <math qid="Q1938">\acosh@@{z} = \ln@{+(z^{2}-1)^{1/2}+z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@@{z} = \ln@{+(z^{2}-1)^{1/2}+z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(z) = ln(+((z)^(2)- 1)^(1/2)+ z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[z] == Log[+((z)^(2)- 1)^(1/2)+ z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.662885893+3.891061519*I
 Test Values: {z = -1/2+1/2*I*3^(1/2), z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.316957897-4.712388980*I
 Test Values: {z = -1/2*3^(1/2)-1/2*I, z = 3/2}</syntaxhighlight><br></div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.37.E19 4.37.E19] || [[Item:Q1938|<math>\acosh@@{z} = \ln@{-(z^{2}-1)^{1/2}+z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@@{z} = \ln@{-(z^{2}-1)^{1/2}+z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(z) = ln(-((z)^(2)- 1)^(1/2)+ z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[z] == Log[-((z)^(2)- 1)^(1/2)+ z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [5 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.316957897+1.570796326*I
+| [https://dlmf.nist.gov/4.37.E19 4.37.E19] || <math qid="Q1938">\acosh@@{z} = \ln@{-(z^{2}-1)^{1/2}+z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@@{z} = \ln@{-(z^{2}-1)^{1/2}+z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(z) = ln(-((z)^(2)- 1)^(1/2)+ z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[z] == Log[-((z)^(2)- 1)^(1/2)+ z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [5 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.316957897+1.570796326*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.662885893-2.392123788*I
 Test Values: {z = 1/2-1/2*I*3^(1/2), z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.924847301
@@ Line 105: / Line 105: @@
 Test Values: {Rule[z, Rational[3, 2]]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E20 4.37.E20] || [[Item:Q1939|<math>\acosh@{\iunit y} = +\tfrac{1}{2}\pi\iunit+\ln@{(y^{2}+1)^{1/2}+ y}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@{\iunit y} = +\tfrac{1}{2}\pi\iunit+\ln@{(y^{2}+1)^{1/2}+ y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(I*y) = +(1)/(2)*Pi*I + ln(((y)^(2)+ 1)^(1/2)+ y)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[I*y] == +Divide[1,2]*Pi*I + Log[((y)^(2)+ 1)^(1/2)+ y]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.389526433-3.141592654*I
+| [https://dlmf.nist.gov/4.37.E20 4.37.E20] || <math qid="Q1939">\acosh@{\iunit y} = +\tfrac{1}{2}\pi\iunit+\ln@{(y^{2}+1)^{1/2}+ y}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@{\iunit y} = +\tfrac{1}{2}\pi\iunit+\ln@{(y^{2}+1)^{1/2}+ y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(I*y) = +(1)/(2)*Pi*I + ln(((y)^(2)+ 1)^(1/2)+ y)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[I*y] == +Divide[1,2]*Pi*I + Log[((y)^(2)+ 1)^(1/2)+ y]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.389526433-3.141592654*I
 Test Values: {y = -1.5, y = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .9624236498-3.141592654*I
 Test Values: {y = -.5, y = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.887270952-3.141592654*I
 Test Values: {y = -2, y = 1/2}</syntaxhighlight><br></div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.37.E20 4.37.E20] || [[Item:Q1939|<math>\acosh@{\iunit y} = -\tfrac{1}{2}\pi\iunit+\ln@{(y^{2}+1)^{1/2}- y}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@{\iunit y} = -\tfrac{1}{2}\pi\iunit+\ln@{(y^{2}+1)^{1/2}- y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(I*y) = -(1)/(2)*Pi*I + ln(((y)^(2)+ 1)^(1/2)- y)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[I*y] == -Divide[1,2]*Pi*I + Log[((y)^(2)+ 1)^(1/2)- y]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.389526433+3.141592654*I
+| [https://dlmf.nist.gov/4.37.E20 4.37.E20] || <math qid="Q1939">\acosh@{\iunit y} = -\tfrac{1}{2}\pi\iunit+\ln@{(y^{2}+1)^{1/2}- y}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@{\iunit y} = -\tfrac{1}{2}\pi\iunit+\ln@{(y^{2}+1)^{1/2}- y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(I*y) = -(1)/(2)*Pi*I + ln(((y)^(2)+ 1)^(1/2)- y)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[I*y] == -Divide[1,2]*Pi*I + Log[((y)^(2)+ 1)^(1/2)- y]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.389526433+3.141592654*I
 Test Values: {y = 1.5, y = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .9624236498+3.141592654*I
 Test Values: {y = .5, y = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.887270952+3.141592654*I
@@ Line 116: / Line 116: @@
 Test Values: {Rule[y, Rational[1, 2]]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E21 4.37.E21] || [[Item:Q1940|<math>\acosh@@{z} = 2\ln@{\left(\frac{z+1}{2}\right)^{1/2}+\left(\frac{z-1}{2}\right)^{1/2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@@{z} = 2\ln@{\left(\frac{z+1}{2}\right)^{1/2}+\left(\frac{z-1}{2}\right)^{1/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(z) = 2*ln(((z + 1)/(2))^(1/2)+((z - 1)/(2))^(1/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[z] == 2*Log[(Divide[z + 1,2])^(1/2)+(Divide[z - 1,2])^(1/2)]</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 1]
+| [https://dlmf.nist.gov/4.37.E21 4.37.E21] || <math qid="Q1940">\acosh@@{z} = 2\ln@{\left(\frac{z+1}{2}\right)^{1/2}+\left(\frac{z-1}{2}\right)^{1/2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@@{z} = 2\ln@{\left(\frac{z+1}{2}\right)^{1/2}+\left(\frac{z-1}{2}\right)^{1/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(z) = 2*ln(((z + 1)/(2))^(1/2)+((z - 1)/(2))^(1/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[z] == 2*Log[(Divide[z + 1,2])^(1/2)+(Divide[z - 1,2])^(1/2)]</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.37.E22 4.37.E22] || [[Item:Q1941|<math>\acosh@@{x} = +\ln@{i(1-x^{2})^{1/2}+x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@@{x} = +\ln@{i(1-x^{2})^{1/2}+x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(x) = + ln(I*(1 - (x)^(2))^(1/2)+ x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[x] == + Log[I*(1 - (x)^(2))^(1/2)+ x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.924847301
+| [https://dlmf.nist.gov/4.37.E22 4.37.E22] || <math qid="Q1941">\acosh@@{x} = +\ln@{i(1-x^{2})^{1/2}+x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@@{x} = +\ln@{i(1-x^{2})^{1/2}+x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(x) = + ln(I*(1 - (x)^(2))^(1/2)+ x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[x] == + Log[I*(1 - (x)^(2))^(1/2)+ x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.924847301
 Test Values: {x = 1.5, x = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.633915796
 Test Values: {x = 2, x = 1/2}</syntaxhighlight><br></div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.37.E22 4.37.E22] || [[Item:Q1941|<math>\acosh@@{x} = -\ln@{i(1-x^{2})^{1/2}+x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@@{x} = -\ln@{i(1-x^{2})^{1/2}+x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(x) = - ln(I*(1 - (x)^(2))^(1/2)+ x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[x] == - Log[I*(1 - (x)^(2))^(1/2)+ x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1347500000e-10+2.094395102*I
+| [https://dlmf.nist.gov/4.37.E22 4.37.E22] || <math qid="Q1941">\acosh@@{x} = -\ln@{i(1-x^{2})^{1/2}+x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@@{x} = -\ln@{i(1-x^{2})^{1/2}+x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(x) = - ln(I*(1 - (x)^(2))^(1/2)+ x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[x] == - Log[I*(1 - (x)^(2))^(1/2)+ x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1347500000e-10+2.094395102*I
 Test Values: {x = .5, x = 1/2}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, 2.0943951023931953]
 Test Values: {Rule[x, Rational[1, 2]]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E23 4.37.E23] || [[Item:Q1942|<math>\acosh@@{x} = +\pi i+\ln@{(x^{2}-1)^{1/2}-x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@@{x} = +\pi i+\ln@{(x^{2}-1)^{1/2}-x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(x) = + Pi*I + ln(((x)^(2)- 1)^(1/2)- x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[x] == + Pi*I + Log[((x)^(2)- 1)^(1/2)- x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.924847301-6.283185308*I
+| [https://dlmf.nist.gov/4.37.E23 4.37.E23] || <math qid="Q1942">\acosh@@{x} = +\pi i+\ln@{(x^{2}-1)^{1/2}-x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@@{x} = +\pi i+\ln@{(x^{2}-1)^{1/2}-x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(x) = + Pi*I + ln(((x)^(2)- 1)^(1/2)- x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[x] == + Pi*I + Log[((x)^(2)- 1)^(1/2)- x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.924847301-6.283185308*I
 Test Values: {x = 1.5, x = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1347500000e-10-4.188790205*I
 Test Values: {x = .5, x = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.633915796-6.283185308*I
 Test Values: {x = 2, x = -2}</syntaxhighlight><br></div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.37.E23 4.37.E23] || [[Item:Q1942|<math>\acosh@@{x} = -\pi i+\ln@{(x^{2}-1)^{1/2}-x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@@{x} = -\pi i+\ln@{(x^{2}-1)^{1/2}-x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(x) = - Pi*I + ln(((x)^(2)- 1)^(1/2)- x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[x] == - Pi*I + Log[((x)^(2)- 1)^(1/2)- x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.924847301+0.*I
+| [https://dlmf.nist.gov/4.37.E23 4.37.E23] || <math qid="Q1942">\acosh@@{x} = -\pi i+\ln@{(x^{2}-1)^{1/2}-x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@@{x} = -\pi i+\ln@{(x^{2}-1)^{1/2}-x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccosh(x) = - Pi*I + ln(((x)^(2)- 1)^(1/2)- x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[x] == - Pi*I + Log[((x)^(2)- 1)^(1/2)- x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.924847301+0.*I
 Test Values: {x = 1.5, x = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1347500000e-10+2.094395103*I
 Test Values: {x = .5, x = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.633915796+0.*I
@@ Line 137: / Line 137: @@
 Test Values: {Rule[x, -2]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E24 4.37.E24] || [[Item:Q1943|<math>\atanh@@{z} = \tfrac{1}{2}\ln@{\frac{1+z}{1-z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atanh@@{z} = \tfrac{1}{2}\ln@{\frac{1+z}{1-z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctanh(z) = (1)/(2)*ln((1 + z)/(1 - z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTanh[z] == Divide[1,2]*Log[Divide[1 + z,1 - z]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2e-9-3.141592654*I
+| [https://dlmf.nist.gov/4.37.E24 4.37.E24] || <math qid="Q1943">\atanh@@{z} = \tfrac{1}{2}\ln@{\frac{1+z}{1-z}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atanh@@{z} = \tfrac{1}{2}\ln@{\frac{1+z}{1-z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctanh(z) = (1)/(2)*ln((1 + z)/(1 - z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTanh[z] == Divide[1,2]*Log[Divide[1 + z,1 - z]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2e-9-3.141592654*I
 Test Values: {z = 1.5, z = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2e-9-3.141592654*I
 Test Values: {z = 2, z = 1/2}</syntaxhighlight><br></div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.37.E25 4.37.E25] || [[Item:Q1944|<math>\atanh@@{x} = +\tfrac{1}{2}\pi i+\tfrac{1}{2}\ln@{\frac{x+1}{x-1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atanh@@{x} = +\tfrac{1}{2}\pi i+\tfrac{1}{2}\ln@{\frac{x+1}{x-1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctanh(x) = +(1)/(2)*Pi*I +(1)/(2)*ln((x + 1)/(x - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTanh[x] == +Divide[1,2]*Pi*I +Divide[1,2]*Log[Divide[x + 1,x - 1]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2e-9-3.141592654*I
+| [https://dlmf.nist.gov/4.37.E25 4.37.E25] || <math qid="Q1944">\atanh@@{x} = +\tfrac{1}{2}\pi i+\tfrac{1}{2}\ln@{\frac{x+1}{x-1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atanh@@{x} = +\tfrac{1}{2}\pi i+\tfrac{1}{2}\ln@{\frac{x+1}{x-1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctanh(x) = +(1)/(2)*Pi*I +(1)/(2)*ln((x + 1)/(x - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTanh[x] == +Divide[1,2]*Pi*I +Divide[1,2]*Log[Divide[x + 1,x - 1]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2e-9-3.141592654*I
 Test Values: {x = 1.5, x = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2e-9-3.141592654*I
 Test Values: {x = .5, x = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2e-9-3.141592654*I
 Test Values: {x = 2, x = -3/2}</syntaxhighlight><br></div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.37.E25 4.37.E25] || [[Item:Q1944|<math>\atanh@@{x} = -\tfrac{1}{2}\pi i+\tfrac{1}{2}\ln@{\frac{x+1}{x-1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atanh@@{x} = -\tfrac{1}{2}\pi i+\tfrac{1}{2}\ln@{\frac{x+1}{x-1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctanh(x) = -(1)/(2)*Pi*I +(1)/(2)*ln((x + 1)/(x - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTanh[x] == -Divide[1,2]*Pi*I +Divide[1,2]*Log[Divide[x + 1,x - 1]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.1102230246251565*^-16, 3.141592653589793]
+| [https://dlmf.nist.gov/4.37.E25 4.37.E25] || <math qid="Q1944">\atanh@@{x} = -\tfrac{1}{2}\pi i+\tfrac{1}{2}\ln@{\frac{x+1}{x-1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atanh@@{x} = -\tfrac{1}{2}\pi i+\tfrac{1}{2}\ln@{\frac{x+1}{x-1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctanh(x) = -(1)/(2)*Pi*I +(1)/(2)*ln((x + 1)/(x - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTanh[x] == -Divide[1,2]*Pi*I +Divide[1,2]*Log[Divide[x + 1,x - 1]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.1102230246251565*^-16, 3.141592653589793]
 Test Values: {Rule[x, Rational[-3, 2]]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E26 4.37.E26] || [[Item:Q1945|<math>z = \sinh@@{w}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \sinh@@{w}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = sinh(w)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == Sinh[w]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .73886869e-2-.1707313589*I
+| [https://dlmf.nist.gov/4.37.E26 4.37.E26] || <math qid="Q1945">z = \sinh@@{w}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \sinh@@{w}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = sinh(w)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == Sinh[w]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .73886869e-2-.1707313589*I
 Test Values: {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.358636717+.1952940451*I
 Test Values: {w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.3586367171-1.536756763*I
@@ Line 157: / Line 157: @@
 Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E27 4.37.E27] || [[Item:Q1946|<math>z = \cosh@@{w}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \cosh@@{w}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = cosh(w)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == Cosh[w]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.3617401130+.309246236e-1*I
+| [https://dlmf.nist.gov/4.37.E27 4.37.E27] || <math qid="Q1946">z = \cosh@@{w}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \cosh@@{w}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = cosh(w)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == Cosh[w]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.3617401130+.309246236e-1*I
 Test Values: {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.727765517+.3969500276*I
 Test Values: {w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.7277655170-1.335100780*I
@@ Line 165: / Line 165: @@
 Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E28 4.37.E28] || [[Item:Q1947|<math>z = \tanh@@{w}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \tanh@@{w}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = tanh(w)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == Tanh[w]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .736226475e-1+.2564398629*I
+| [https://dlmf.nist.gov/4.37.E28 4.37.E28] || <math qid="Q1947">z = \tanh@@{w}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \tanh@@{w}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = tanh(w)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == Tanh[w]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .736226475e-1+.2564398629*I
 Test Values: {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.292402756+.6224652669*I
 Test Values: {w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2924027565-1.109585541*I
@@ Line 173: / Line 173: @@
 Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E29 4.37.E29] || [[Item:Q1948|<math>w = \Asinh@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \Asinh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == ArcSinh[z]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.03458245825512818, 0.12526556729125993]
+| [https://dlmf.nist.gov/4.37.E29 4.37.E29] || <math qid="Q1948">w = \Asinh@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \Asinh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == ArcSinh[z]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.03458245825512818, 0.12526556729125993]
 Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.524504352246847, -0.28539816339744856]
 Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E29 4.37.E29] || [[Item:Q1948|<math>\Asinh@@{z} = (-1)^{k}\asinh@@{z}+k\pi i</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Asinh@@{z} = (-1)^{k}\asinh@@{z}+k\pi i</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[z] == (- 1)^(k)* ArcSinh[z]+ k*Pi*I</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.662885891058621, -2.392123788172313]
+| [https://dlmf.nist.gov/4.37.E29 4.37.E29] || <math qid="Q1948">\Asinh@@{z} = (-1)^{k}\asinh@@{z}+k\pi i</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Asinh@@{z} = (-1)^{k}\asinh@@{z}+k\pi i</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[z] == (- 1)^(k)* ArcSinh[z]+ k*Pi*I</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.662885891058621, -2.392123788172313]
 Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.0, -6.283185307179586]
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E30 4.37.E30] || [[Item:Q1949|<math>w = \Acosh@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \Acosh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == ArcCosh[z]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.20754645532203042, -0.28539816339744833]
+| [https://dlmf.nist.gov/4.37.E30 4.37.E30] || <math qid="Q1949">w = \Acosh@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \Acosh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == ArcCosh[z]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.20754645532203042, -0.28539816339744833]
 Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.03458245825512796, -1.4455307595036366]
 Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E30 4.37.E30] || [[Item:Q1949|<math>\Acosh@@{z} = +\acosh@@{z}+2k\pi i</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acosh@@{z} = +\acosh@@{z}+2k\pi i</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[z] == + ArcCosh[z]+ 2*k*Pi*I</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, -6.283185307179586]
+| [https://dlmf.nist.gov/4.37.E30 4.37.E30] || <math qid="Q1949">\Acosh@@{z} = +\acosh@@{z}+2k\pi i</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acosh@@{z} = +\acosh@@{z}+2k\pi i</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[z] == + ArcCosh[z]+ 2*k*Pi*I</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, -6.283185307179586]
 Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.0, -12.566370614359172]
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E30 4.37.E30] || [[Item:Q1949|<math>\Acosh@@{z} = -\acosh@@{z}+2k\pi i</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acosh@@{z} = -\acosh@@{z}+2k\pi i</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[z] == - ArcCosh[z]+ 2*k*Pi*I</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.3169578969248166, -4.71238898038469]
+| [https://dlmf.nist.gov/4.37.E30 4.37.E30] || <math qid="Q1949">\Acosh@@{z} = -\acosh@@{z}+2k\pi i</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acosh@@{z} = -\acosh@@{z}+2k\pi i</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[z] == - ArcCosh[z]+ 2*k*Pi*I</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.3169578969248166, -4.71238898038469]
 Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.3169578969248166, -10.995574287564276]
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E31 4.37.E31] || [[Item:Q1950|<math>w = \Atanh@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \Atanh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == ArcTanh[z]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [10 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.3167192594503839, 0.49999999999999994]
+| [https://dlmf.nist.gov/4.37.E31 4.37.E31] || <math qid="Q1950">w = \Atanh@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \Atanh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == ArcTanh[z]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [10 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.3167192594503839, 0.49999999999999994]
 Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Rational[1, 2]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.0493061443340546, 0.8660254037844387]
 Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[z, Rational[1, 2]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/4.37.E31 4.37.E31] || [[Item:Q1950|<math>\Atanh@@{z} = \atanh@@{z}+k\pi i</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Atanh@@{z} = \atanh@@{z}+k\pi i</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTanh[z] == ArcTanh[z]+ k*Pi*I</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, -3.141592653589793]
+| [https://dlmf.nist.gov/4.37.E31 4.37.E31] || <math qid="Q1950">\Atanh@@{z} = \atanh@@{z}+k\pi i</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Atanh@@{z} = \atanh@@{z}+k\pi i</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTanh[z] == ArcTanh[z]+ k*Pi*I</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, -3.141592653589793]
 Test Values: {Rule[k, 1], Rule[z, Rational[1, 2]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.0, -6.283185307179586]
 Test Values: {Rule[k, 2], Rule[z, Rational[1, 2]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |}
 </div>

4.37: Difference between revisions

Latest revision as of 11:10, 28 June 2021

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