4.23: Difference between revisions

Latest revision as of 11:07, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
4.23.E1	${\displaystyle{\displaystyle\operatorname{Arcsin}z=\int_{0}^{z}\frac{\mathrm{d% }t}{(1-t^{2})^{1/2}}}}$ `\Asin@@{z} = \int_{0}^{z}\frac{\diff{t}}{(1-t^{2})^{1/2}}`		Error	ArcSin[z] == Integrate[Divide[1,(1 - (t)^(2))^(1/2)], {t, 0, z}, GenerateConditions->None]	Missing Macro Error	Successful	-	Successful [Tested: 7]
4.23.E2	${\displaystyle{\displaystyle\operatorname{Arccos}z=\int_{z}^{1}\frac{\mathrm{d% }t}{(1-t^{2})^{1/2}}}}$ `\Acos@@{z} = \int_{z}^{1}\frac{\diff{t}}{(1-t^{2})^{1/2}}`		Error	ArcCos[z] == Integrate[Divide[1,(1 - (t)^(2))^(1/2)], {t, z, 1}, GenerateConditions->None]	Missing Macro Error	Successful	-	Successful [Tested: 7]
4.23.E3	${\displaystyle{\displaystyle\operatorname{Arctan}z=\int_{0}^{z}\frac{\mathrm{d% }t}{1+t^{2}}}}$ `\Atan@@{z} = \int_{0}^{z}\frac{\diff{t}}{1+t^{2}}`		Error	ArcTan[z] == Integrate[Divide[1,1 + (t)^(2)], {t, 0, z}, GenerateConditions->None]	Missing Macro Error	Successful	-	Successful [Tested: 1]
4.23.E4	${\displaystyle{\displaystyle\operatorname{Arccsc}z=\operatorname{Arcsin}\left(% 1/z\right)}}$ `\Acsc@@{z} = \Asin@{1/z}`		Error	ArcCsc[z] == ArcSin[1/z]	Missing Macro Error	Successful	-	Successful [Tested: 7]
4.23.E5	${\displaystyle{\displaystyle\operatorname{Arcsec}z=\operatorname{Arccos}\left(% 1/z\right)}}$ `\Asec@@{z} = \Acos@{1/z}`		Error	ArcSec[z] == ArcCos[1/z]	Missing Macro Error	Successful	-	Successful [Tested: 7]
4.23.E6	${\displaystyle{\displaystyle\operatorname{Arccot}z=\operatorname{Arctan}\left(% 1/z\right)}}$ `\Acot@@{z} = \Atan@{1/z}`		Error	ArcCot[z] == ArcTan[1/z]	Missing Macro Error	Successful	-	Successful [Tested: 7]
4.23.E7	${\displaystyle{\displaystyle\operatorname{arccsc}z=\operatorname{arcsin}\left(% 1/z\right)}}$ `\acsc@@{z} = \asin@{1/z}`		arccsc(z) = arcsin(1/z)	ArcCsc[z] == ArcSin[1/z]	Failure	Successful	Successful [Tested: 7]	Successful [Tested: 7]
4.23.E8	${\displaystyle{\displaystyle\operatorname{arcsec}z=\operatorname{arccos}\left(% 1/z\right)}}$ `\asec@@{z} = \acos@{1/z}`		arcsec(z) = arccos(1/z)	ArcSec[z] == ArcCos[1/z]	Failure	Successful	Successful [Tested: 7]	Successful [Tested: 7]
4.23.E9	${\displaystyle{\displaystyle\operatorname{arccot}z=\operatorname{arctan}\left(% 1/z\right)}}$ `\acot@@{z} = \atan@{1/z}`		arccot(z) = arctan(1/z)	ArcCot[z] == ArcTan[1/z]	Failure	Successful	Failed [2 / 7] Result: 3.141592654+0.I Test Values: {z = -1/2+1/2I3^(1/2), z = 1/2} Result: 3.141592654+0.I Test Values: {z = -1/23^(1/2)-1/2I, z = 1/2}	Successful [Tested: 1]
4.23.E10	${\displaystyle{\displaystyle\operatorname{arcsin}\left(-z\right)=-% \operatorname{arcsin}z}}$ `\asin@{-z} = -\asin@@{z}`		arcsin(- z) = - arcsin(z)	ArcSin[- z] == - ArcSin[z]	Successful	Successful	-	Successful [Tested: 7]
4.23.E11	${\displaystyle{\displaystyle\operatorname{arccos}\left(-z\right)=\pi-% \operatorname{arccos}z}}$ `\acos@{-z} = \pi-\acos@@{z}`		arccos(- z) = Pi - arccos(z)	ArcCos[- z] == Pi - ArcCos[z]	Successful	Successful	-	Successful [Tested: 7]
4.23.E12	${\displaystyle{\displaystyle\operatorname{arctan}\left(-z\right)=-% \operatorname{arctan}z}}$ `\atan@{-z} = -\atan@@{z}`		arctan(- z) = - arctan(z)	ArcTan[- z] == - ArcTan[z]	Successful	Successful	-	Successful [Tested: 1]
4.23.E13	${\displaystyle{\displaystyle\operatorname{arccsc}\left(-z\right)=-% \operatorname{arccsc}z}}$ `\acsc@{-z} = -\acsc@@{z}`		arccsc(- z) = - arccsc(z)	ArcCsc[- z] == - ArcCsc[z]	Successful	Successful	-	Successful [Tested: 7]
4.23.E14	${\displaystyle{\displaystyle\operatorname{arcsec}\left(-z\right)=\pi-% \operatorname{arcsec}z}}$ `\asec@{-z} = \pi-\asec@@{z}`		arcsec(- z) = Pi - arcsec(z)	ArcSec[- z] == Pi - ArcSec[z]	Successful	Successful	-	Successful [Tested: 7]
4.23.E15	${\displaystyle{\displaystyle\operatorname{arccot}\left(-z\right)=-% \operatorname{arccot}z}}$ `\acot@{-z} = -\acot@@{z}`		arccot(- z) = - arccot(z)	ArcCot[- z] == - ArcCot[z]	Failure	Successful	Skip - No test values generated	Successful [Tested: 1]
4.23.E16	${\displaystyle{\displaystyle\operatorname{arccos}z=\tfrac{1}{2}\pi-% \operatorname{arcsin}z}}$ `\acos@@{z} = \tfrac{1}{2}\pi-\asin@@{z}`		arccos(z) = (1)/(2)*Pi - arcsin(z)	ArcCos[z] == Divide[1,2]*Pi - ArcSin[z]	Failure	Successful	Successful [Tested: 7]	Successful [Tested: 7]
4.23.E17	${\displaystyle{\displaystyle\operatorname{arcsec}z=\tfrac{1}{2}\pi-% \operatorname{arccsc}z}}$ `\asec@@{z} = \tfrac{1}{2}\pi-\acsc@@{z}`		arcsec(z) = (1)/(2)*Pi - arccsc(z)	ArcSec[z] == Divide[1,2]*Pi - ArcCsc[z]	Failure	Successful	Successful [Tested: 7]	Successful [Tested: 7]
4.23.E18	${\displaystyle{\displaystyle\operatorname{arccot}z=+\tfrac{1}{2}\pi-% \operatorname{arctan}z}}$ `\acot@@{z} = +\tfrac{1}{2}\pi-\atan@@{z}`		arccot(z) = +(1)/(2)*Pi - arctan(z)	ArcCot[z] == +Divide[1,2]*Pi - ArcTan[z]	Successful	Failure	Skip - symbolical successful subtest	Successful [Tested: 1]
4.23.E18	${\displaystyle{\displaystyle\operatorname{arccot}z=-\tfrac{1}{2}\pi-% \operatorname{arctan}z}}$ `\acot@@{z} = -\tfrac{1}{2}\pi-\atan@@{z}`		arccot(z) = -(1)/(2)*Pi - arctan(z)	ArcCot[z] == -Divide[1,2]*Pi - ArcTan[z]	Failure	Failure	Failed [7 / 7] Result: 3.141592654+0.I Test Values: {z = 1/23^(1/2)+1/2I, z = 1/2} Result: 3.141592654+0.I Test Values: {z = -1/2+1/2I3^(1/2), z = 1/2} Result: 3.141592654+0.I Test Values: {z = 1/2-1/2I3^(1/2), z = 1/2} Result: 3.141592654+0.I Test Values: {z = -1/23^(1/2)-1/2I, z = 1/2} ... skip entries to safe data	Failed [1 / 1] Result: 3.141592653589793 Test Values: {Rule[z, Rational[1, 2]]}
4.23.E19	${\displaystyle{\displaystyle\operatorname{arcsin}z=-i\ln\left((1-z^{2})^{1/2}+% iz\right)}}$ `\asin@@{z} = -i\ln@{(1-z^{2})^{1/2}+iz}`		arcsin(z) = - Iln((1 - (z)^(2))^(1/2)+ Iz)	ArcSin[z] == - ILog[(1 - (z)^(2))^(1/2)+ Iz]	Failure	Successful	Successful [Tested: 7]	Successful [Tested: 7]
4.23.E20	${\displaystyle{\displaystyle\operatorname{arcsin}x=\tfrac{1}{2}\pi+i\ln\left((% x^{2}-1)^{1/2}+x\right)}}$ `\asin@@{x} = \tfrac{1}{2}\pi+ i\ln@{(x^{2}-1)^{1/2}+x}`		arcsin(x) = (1)/(2)Pi + Iln(((x)^(2)- 1)^(1/2)+ x)	ArcSin[x] == Divide[1,2]Pi + ILog[((x)^(2)- 1)^(1/2)+ x]	Failure	Failure	Failed [2 / 3] Result: 0.-1.924847300I Test Values: {x = 1.5, x = 3/2} Result: 0.-2.633915794I Test Values: {x = 2, x = 3/2}	Failed [1 / 1] Result: Complex[0.0, -1.9248473002384139] Test Values: {Rule[x, Rational[3, 2]]}
4.23.E20	${\displaystyle{\displaystyle\operatorname{arcsin}x=\tfrac{1}{2}\pi-i\ln\left((% x^{2}-1)^{1/2}+x\right)}}$ `\asin@@{x} = \tfrac{1}{2}\pi- i\ln@{(x^{2}-1)^{1/2}+x}`		arcsin(x) = (1)/(2)Pi - Iln(((x)^(2)- 1)^(1/2)+ x)	ArcSin[x] == Divide[1,2]Pi - ILog[((x)^(2)- 1)^(1/2)+ x]	Failure	Failure	Failed [1 / 3] Result: -2.094395102+.1347500000e-10*I Test Values: {x = .5, x = 3/2}	Successful [Tested: 1]
4.23.E21	${\displaystyle{\displaystyle\operatorname{arcsin}x=-\tfrac{1}{2}\pi+i\ln\left(% (x^{2}-1)^{1/2}-x\right)}}$ `\asin@@{x} = -\tfrac{1}{2}\pi+ i\ln@{(x^{2}-1)^{1/2}-x}`		arcsin(x) = -(1)/(2)Pi + Iln(((x)^(2)- 1)^(1/2)- x)	ArcSin[x] == -Divide[1,2]Pi + ILog[((x)^(2)- 1)^(1/2)- x]	Failure	Failure	Failed [3 / 3] Result: 6.283185308+.7e-9I Test Values: {x = 1.5, x = -2} Result: 4.188790205-.1347500000e-10I Test Values: {x = .5, x = -2} Result: 6.283185308+.2e-8*I Test Values: {x = 2, x = -2}	Successful [Tested: 1]
4.23.E21	${\displaystyle{\displaystyle\operatorname{arcsin}x=-\tfrac{1}{2}\pi-i\ln\left(% (x^{2}-1)^{1/2}-x\right)}}$ `\asin@@{x} = -\tfrac{1}{2}\pi- i\ln@{(x^{2}-1)^{1/2}-x}`		arcsin(x) = -(1)/(2)Pi - Iln(((x)^(2)- 1)^(1/2)- x)	ArcSin[x] == -Divide[1,2]Pi - ILog[((x)^(2)- 1)^(1/2)- x]	Failure	Failure	Failed [2 / 3] Result: 0.-1.924847301I Test Values: {x = 1.5, x = -2} Result: 0.-2.633915796I Test Values: {x = 2, x = -2}	Failed [1 / 1] Result: Complex[0.0, 2.633915793849633] Test Values: {Rule[x, -2]}
4.23.E22	${\displaystyle{\displaystyle\operatorname{arccos}z=\tfrac{1}{2}\pi+i\ln\left((% 1-z^{2})^{1/2}+iz\right)}}$ `\acos@@{z} = \tfrac{1}{2}\pi+i\ln@{(1-z^{2})^{1/2}+iz}`		arccos(z) = (1)/(2)Pi + Iln((1 - (z)^(2))^(1/2)+ I*z)	ArcCos[z] == Divide[1,2]Pi + ILog[(1 - (z)^(2))^(1/2)+ I*z]	Failure	Successful	Successful [Tested: 7]	Successful [Tested: 7]
4.23.E23	${\displaystyle{\displaystyle\operatorname{arccos}z=-2i\ln\left(\left(\frac{1+z% }{2}\right)^{1/2}+i\left(\frac{1-z}{2}\right)^{1/2}\right)}}$ `\acos@@{z} = -2i\ln@{\left(\frac{1+z}{2}\right)^{1/2}+i\left(\frac{1-z}{2}\right)^{1/2}}`		arccos(z) = - 2Iln(((1 + z)/(2))^(1/2)+ I*((1 - z)/(2))^(1/2))	ArcCos[z] == - 2ILog[(Divide[1 + z,2])^(1/2)+ I*(Divide[1 - z,2])^(1/2)]	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
4.23.E24	${\displaystyle{\displaystyle\operatorname{arccos}x=-i\ln\left((x^{2}-1)^{1/2}+% x\right)}}$ `\acos@@{x} = - i\ln@{(x^{2}-1)^{1/2}+x}`		arccos(x) = - I*ln(((x)^(2)- 1)^(1/2)+ x)	ArcCos[x] == - I*Log[((x)^(2)- 1)^(1/2)+ x]	Failure	Failure	Failed [2 / 3] Result: 1.924847300I Test Values: {x = 1.5, x = 3/2} Result: 2.633915794I Test Values: {x = 2, x = 3/2}	Failed [1 / 1] Result: Complex[0.0, 1.9248473002384139] Test Values: {Rule[x, Rational[3, 2]]}
4.23.E24	${\displaystyle{\displaystyle\operatorname{arccos}x=+i\ln\left((x^{2}-1)^{1/2}+% x\right)}}$ `\acos@@{x} = + i\ln@{(x^{2}-1)^{1/2}+x}`		arccos(x) = + I*ln(((x)^(2)- 1)^(1/2)+ x)	ArcCos[x] == + I*Log[((x)^(2)- 1)^(1/2)+ x]	Failure	Failure	Failed [1 / 3] Result: 2.094395102-.1347500000e-10*I Test Values: {x = .5, x = 3/2}	Successful [Tested: 1]
4.23.E25	${\displaystyle{\displaystyle\operatorname{arccos}x=\pi-i\ln\left((x^{2}-1)^{1/% 2}-x\right)}}$ `\acos@@{x} = \pi- i\ln@{(x^{2}-1)^{1/2}-x}`		arccos(x) = Pi - I*ln(((x)^(2)- 1)^(1/2)- x)	ArcCos[x] == Pi - I*Log[((x)^(2)- 1)^(1/2)- x]	Failure	Failure	Failed [3 / 3] Result: -6.283185308-.7e-9I Test Values: {x = 1.5, x = -2} Result: -4.188790205+.1347500000e-10I Test Values: {x = .5, x = -2} Result: -6.283185308-.2e-8*I Test Values: {x = 2, x = -2}	Successful [Tested: 1]
4.23.E25	${\displaystyle{\displaystyle\operatorname{arccos}x=\pi+i\ln\left((x^{2}-1)^{1/% 2}-x\right)}}$ `\acos@@{x} = \pi+ i\ln@{(x^{2}-1)^{1/2}-x}`		arccos(x) = Pi + I*ln(((x)^(2)- 1)^(1/2)- x)	ArcCos[x] == Pi + I*Log[((x)^(2)- 1)^(1/2)- x]	Failure	Failure	Failed [2 / 3] Result: 0.+1.924847301I Test Values: {x = 1.5, x = -2} Result: 0.+2.633915796I Test Values: {x = 2, x = -2}	Failed [1 / 1] Result: Complex[0.0, -2.633915793849633] Test Values: {Rule[x, -2]}
4.23.E26	${\displaystyle{\displaystyle\operatorname{arctan}z=\frac{i}{2}\ln\left(\frac{i% +z}{i-z}\right)}}$ `\atan@@{z} = \frac{i}{2}\ln@{\frac{i+z}{i-z}}`		arctan(z) = (I)/(2)*ln((I + z)/(I - z))	ArcTan[z] == Divide[I,2]*Log[Divide[I + z,I - z]]	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
4.23.E27	${\displaystyle{\displaystyle\operatorname{arctan}\left(iy\right)=+\frac{1}{2}% \pi+\frac{i}{2}\ln\left(\frac{y+1}{y-1}\right)}}$ `\atan@{iy} = +\frac{1}{2}\pi+\frac{i}{2}\ln@{\frac{y+1}{y-1}}`		arctan(Iy) = +(1)/(2)Pi +(I)/(2)*ln((y + 1)/(y - 1))	ArcTan[Iy] == +Divide[1,2]Pi +Divide[I,2]*Log[Divide[y + 1,y - 1]]	Failure	Failure	Failed [2 / 6] Result: -3.141592654-.2e-9I Test Values: {y = -1.5, y = -3/2} Result: -3.141592654+.2e-9I Test Values: {y = -2, y = -3/2}	Failed [1 / 1] Result: Complex[-3.141592653589793, -1.1102230246251565*^-16] Test Values: {Rule[y, Rational[-3, 2]]}
4.23.E27	${\displaystyle{\displaystyle\operatorname{arctan}\left(iy\right)=-\frac{1}{2}% \pi+\frac{i}{2}\ln\left(\frac{y+1}{y-1}\right)}}$ `\atan@{iy} = -\frac{1}{2}\pi+\frac{i}{2}\ln@{\frac{y+1}{y-1}}`		arctan(Iy) = -(1)/(2)Pi +(I)/(2)*ln((y + 1)/(y - 1))	ArcTan[Iy] == -Divide[1,2]Pi +Divide[I,2]*Log[Divide[y + 1,y - 1]]	Failure	Failure	Failed [4 / 6] Result: 3.141592654+.2e-9I Test Values: {y = 1.5, y = -3/2} Result: 3.141592654+.2e-9I Test Values: {y = -.5, y = -3/2} Result: 3.141592654-.2e-9I Test Values: {y = .5, y = -3/2} Result: 3.141592654-.2e-9I Test Values: {y = 2, y = -3/2}	Successful [Tested: 1]
4.23.E28	${\displaystyle{\displaystyle z=\sin w}}$ `z = \sin@@{w}`		z = sin(w)	z == Sin[w]	Failure	Failure	Failed [70 / 70] Result: .70450695e-2+.1624035369I Test Values: {w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -1.358980334+.5284289409I Test Values: {w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} Result: -.3589803345-1.203621867I Test Values: {w = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)} Result: -1.725005738-.8375964631I 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[0.007045069484300837, 0.16240353677712993] 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[-1.3589803343001376, 0.5284289405615687] 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
4.23.E29	${\displaystyle{\displaystyle z=\cos w}}$ `z = \cos@@{w}`		z = cos(w)	z == Cos[w]	Failure	Failure	Failed [70 / 70] Result: .1354823851+.8969495503I Test Values: {w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -1.230543019+1.262974954I Test Values: {w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} Result: -.2305430189-.4690758537I Test Values: {w = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)} Result: -1.596568423-.1030504497I 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[0.13548238472721352, 0.8969495502290324] 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[-1.230543019057225, 1.2629749540134712] 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
4.23.E30	${\displaystyle{\displaystyle z=\tan w}}$ `z = \tan@@{w}`		z = tan(w)	z == Tan[w]	Failure	Failure	Failed [70 / 70] Result: .1520945236-.3500402975I Test Values: {w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -1.213930880+.159851065e-1I Test Values: {w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} Result: -.2139308804-1.716065702I Test Values: {w = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)} Result: -1.579956284-1.350040298I 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[0.1520945235384168, -0.3500402971922752] 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[-1.2139308802460218, 0.015985106592163567] 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
4.23.E31	${\displaystyle{\displaystyle w=\operatorname{Arcsin}z}}$ `w = \Asin@@{z}`		Error	w == ArcSin[z]	Missing Macro Error	Failure	-	Failed [70 / 70] Result: Complex[0.0806272403869902, -0.15847894846240845] 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[1.2407598364931787, -0.3314429455293106] 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
4.23.E31	${\displaystyle{\displaystyle\operatorname{Arcsin}z=(-1)^{k}\operatorname{% arcsin}z+k\pi}}$ `\Asin@@{z} = (-1)^{k}\asin@@{z}+k\pi`		Error	ArcSin[z] == (- 1)^(k)* ArcSin[z]+ k*Pi	Missing Macro Error	Failure	-	Failed [21 / 21] Result: Complex[-1.5707963267948961, 1.3169578969248168] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: -6.283185307179586 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
4.23.E32	${\displaystyle{\displaystyle w=\operatorname{Arccos}z}}$ `w = \Acos@@{z}`		Error	w == ArcCos[z]	Missing Macro Error	Failure	-	Failed [70 / 70] Result: Complex[0.08062724038699065, 1.1584789484624083] 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[-1.0795053557191978, 1.3314429455293104] 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
4.23.E32	${\displaystyle{\displaystyle\operatorname{Arccos}z=+\operatorname{arccos}z+2k% \pi}}$ `\Acos@@{z} = +\acos@@{z}+2k\pi`		Error	ArcCos[z] == + ArcCos[z]+ 2kPi	Missing Macro Error	Failure	-	Failed [21 / 21] Result: -6.283185307179586 Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: -12.566370614359172 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
4.23.E32	${\displaystyle{\displaystyle\operatorname{Arccos}z=-\operatorname{arccos}z+2k% \pi}}$ `\Acos@@{z} = -\acos@@{z}+2k\pi`		Error	ArcCos[z] == - ArcCos[z]+ 2kPi	Missing Macro Error	Failure	-	Failed [21 / 21] Result: Complex[-4.71238898038469, -1.3169578969248168] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-10.995574287564276, -1.3169578969248168] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
4.23.E33	${\displaystyle{\displaystyle w=\operatorname{Arctan}z}}$ `w = \Atan@@{z}`		Error	w == ArcTan[z]	Missing Macro Error	Failure	-	Failed [10 / 10] Result: Complex[0.4023777947836326, 0.49999999999999994] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Rational[1, 2]]} Result: Complex[-0.9636476090008059, 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
4.23.E33	${\displaystyle{\displaystyle\operatorname{Arctan}z=\operatorname{arctan}z+k\pi}}$ `\Atan@@{z} = \atan@@{z}+k\pi`		Error	ArcTan[z] == ArcTan[z]+ k*Pi	Missing Macro Error	Failure	-	Failed [3 / 3] Result: -3.141592653589793 Test Values: {Rule[k, 1], Rule[z, Rational[1, 2]]} Result: -6.283185307179586 Test Values: {Rule[k, 2], Rule[z, Rational[1, 2]]} ... skip entries to safe data
4.23.E34	${\displaystyle{\displaystyle\operatorname{arcsin}z=\operatorname{arcsin}\beta+% \mathrm{i}\operatorname{sign}\left(y\right)\ln\left(\alpha+(\alpha^{2}-1)^{1/2% }\right)}}$ `\asin@@{z} = \asin@@{\beta}+\iunit\sign@{y}\ln@{\alpha+(\alpha^{2}-1)^{1/2}}`		arcsin(x + yI) = arcsin((1)/(2)((x + 1)^(2)+ (y)^(2))^(1/2)-(1)/(2)((x - 1)^(2)+ (y)^(2))^(1/2))+ Isignum(y)ln(((1)/(2)((x + 1)^(2)+ (y)^(2))^(1/2)+(1)/(2)((x - 1)^(2)+ (y)^(2))^(1/2))+(((1)/(2)((x + 1)^(2)+ (y)^(2))^(1/2)+(1)/(2)*((x - 1)^(2)+ (y)^(2))^(1/2))^(2)- 1)^(1/2))	ArcSin[x + yI] == ArcSin[Divide[1,2]((x + 1)^(2)+ (y)^(2))^(1/2)-Divide[1,2]((x - 1)^(2)+ (y)^(2))^(1/2)]+ ISign[y]Log[(Divide[1,2]((x + 1)^(2)+ (y)^(2))^(1/2)+Divide[1,2]((x - 1)^(2)+ (y)^(2))^(1/2))+((Divide[1,2]((x + 1)^(2)+ (y)^(2))^(1/2)+Divide[1,2]*((x - 1)^(2)+ (y)^(2))^(1/2))^(2)- 1)^(1/2)]	Failure	Failure	Successful [Tested: 18]	Successful [Tested: 18]
4.23.E35	${\displaystyle{\displaystyle\operatorname{arccos}z=\operatorname{arccos}\beta-% \mathrm{i}\operatorname{sign}\left(y\right)\ln\left(\alpha+(\alpha^{2}-1)^{1/2% }\right)}}$ `\acos@@{z} = \acos@@{\beta}-\iunit\sign@{y}\ln@{\alpha+(\alpha^{2}-1)^{1/2}}`		arccos(x + yI) = arccos((1)/(2)((x + 1)^(2)+ (y)^(2))^(1/2)-(1)/(2)((x - 1)^(2)+ (y)^(2))^(1/2))- Isignum(y)ln(((1)/(2)((x + 1)^(2)+ (y)^(2))^(1/2)+(1)/(2)((x - 1)^(2)+ (y)^(2))^(1/2))+(((1)/(2)((x + 1)^(2)+ (y)^(2))^(1/2)+(1)/(2)*((x - 1)^(2)+ (y)^(2))^(1/2))^(2)- 1)^(1/2))	ArcCos[x + yI] == ArcCos[Divide[1,2]((x + 1)^(2)+ (y)^(2))^(1/2)-Divide[1,2]((x - 1)^(2)+ (y)^(2))^(1/2)]- ISign[y]Log[(Divide[1,2]((x + 1)^(2)+ (y)^(2))^(1/2)+Divide[1,2]((x - 1)^(2)+ (y)^(2))^(1/2))+((Divide[1,2]((x + 1)^(2)+ (y)^(2))^(1/2)+Divide[1,2]*((x - 1)^(2)+ (y)^(2))^(1/2))^(2)- 1)^(1/2)]	Failure	Failure	Successful [Tested: 18]	Successful [Tested: 18]
4.23.E36	${\displaystyle{\displaystyle\operatorname{arctan}z=\tfrac{1}{2}\operatorname{% arctan}\left(\frac{2x}{1-x^{2}-y^{2}}\right)+\tfrac{1}{4}i\ln\left(\frac{x^{2}% +(y+1)^{2}}{x^{2}+(y-1)^{2}}\right)}}$ `\atan@@{z} = \tfrac{1}{2}\atan@{\frac{2x}{1-x^{2}-y^{2}}}+\tfrac{1}{4}i\ln@{\frac{x^{2}+(y+1)^{2}}{x^{2}+(y-1)^{2}}}`		arctan(x + yI) = (1)/(2)arctan((2x)/(1 - (x)^(2)- (y)^(2)))+(1)/(4)I*ln(((x)^(2)+(y + 1)^(2))/((x)^(2)+(y - 1)^(2)))	ArcTan[x + yI] == Divide[1,2]ArcTan[Divide[2x,1 - (x)^(2)- (y)^(2)]]+Divide[1,4]I*Log[Divide[(x)^(2)+(y + 1)^(2),(x)^(2)+(y - 1)^(2)]]	Failure	Failure	Failed [16 / 18] Result: 1.570796327-.1e-9I Test Values: {x = 1.5, y = -1.5} Result: 1.570796327-.1e-9I Test Values: {x = 1.5, y = 1.5} Result: 1.570796327+0.I Test Values: {x = 1.5, y = -.5} Result: 1.570796327+0.I Test Values: {x = 1.5, y = .5} ... skip entries to safe data	Failed [16 / 18] Result: Complex[1.5707963267948968, 1.1102230246251565^-16] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: Complex[1.5707963267948968, -1.6653345369377348^-16] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
4.23.E39	${\displaystyle{\displaystyle\operatorname{gd}\left(x\right)=\int_{0}^{x}% \operatorname{sech}t\mathrm{d}t}}$ `\Gudermannian@{x} = \int_{0}^{x}\sech@@{t}\diff{t}`	${\displaystyle{\displaystyle-\infty<x,x<\infty}}$	arctan(sinh(x)) = int(sech(t), t = 0..x)	Gudermannian[x] == Integrate[Sech[t], {t, 0, x}, GenerateConditions->None]	Successful	Aborted	-	Successful [Tested: 3]
4.23.E40	${\displaystyle{\displaystyle\operatorname{gd}\left(x\right)=2\operatorname{% arctan}\left(e^{x}\right)-\tfrac{1}{2}\pi\\ }}$ `\Gudermannian@{x} = 2\atan@{e^{x}}-\tfrac{1}{2}\pi\\`	${\displaystyle{\displaystyle-\infty<x,x<\infty}}$	arctan(sinh(x)) = 2arctan(exp(x))-(1)/(2)Pi	Gudermannian[x] == 2ArcTan[Exp[x]]-Divide[1,2]Pi	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
4.23.E40	${\displaystyle{\displaystyle 2\operatorname{arctan}\left(e^{x}\right)-\tfrac{1% }{2}\pi\\ =\operatorname{arcsin}\left(\tanh x\right)}}$ `2\atan@{e^{x}}-\tfrac{1}{2}\pi\\ = \asin@{\tanh@@{x}}`	${\displaystyle{\displaystyle-\infty<x,x<\infty}}$	2arctan(exp(x))-(1)/(2)Pi = arcsin(tanh(x))	2ArcTan[Exp[x]]-Divide[1,2]Pi == ArcSin[Tanh[x]]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
4.23.E40	${\displaystyle{\displaystyle\operatorname{arcsin}\left(\tanh x\right)=% \operatorname{arccsc}\left(\coth x\right)\\ }}$ `\asin@{\tanh@@{x}} = \acsc@{\coth@@{x}}\\`	${\displaystyle{\displaystyle-\infty<x,x<\infty}}$	arcsin(tanh(x)) = arccsc(coth(x))	ArcSin[Tanh[x]] == ArcCsc[Coth[x]]	Failure	Successful	Successful [Tested: 3]	Successful [Tested: 3]
4.23.E40	${\displaystyle{\displaystyle\operatorname{arccsc}\left(\coth x\right)\\ =\operatorname{arccos}\left(\operatorname{sech}x\right)}}$ `\acsc@{\coth@@{x}}\\ = \acos@{\sech@@{x}}`	${\displaystyle{\displaystyle-\infty<x,x<\infty}}$	arccsc(coth(x)) = arccos(sech(x))	ArcCsc[Coth[x]] == ArcCos[Sech[x]]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
4.23.E40	${\displaystyle{\displaystyle\operatorname{arccos}\left(\operatorname{sech}x% \right)=\operatorname{arcsec}\left(\cosh x\right)\\ }}$ `\acos@{\sech@@{x}} = \asec@{\cosh@@{x}}\\`	${\displaystyle{\displaystyle-\infty<x,x<\infty}}$	arccos(sech(x)) = arcsec(cosh(x))	ArcCos[Sech[x]] == ArcSec[Cosh[x]]	Failure	Successful	Successful [Tested: 3]	Successful [Tested: 3]
4.23.E40	${\displaystyle{\displaystyle\operatorname{arcsec}\left(\cosh x\right)\\ =\operatorname{arctan}\left(\sinh x\right)}}$ `\asec@{\cosh@@{x}}\\ = \atan@{\sinh@@{x}}`	${\displaystyle{\displaystyle-\infty<x,x<\infty}}$	arcsec(cosh(x)) = arctan(sinh(x))	ArcSec[Cosh[x]] == ArcTan[Sinh[x]]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
4.23.E40	${\displaystyle{\displaystyle\operatorname{arctan}\left(\sinh x\right)=% \operatorname{arccot}\left(\operatorname{csch}x\right)}}$ `\atan@{\sinh@@{x}} = \acot@{\csch@@{x}}`	${\displaystyle{\displaystyle-\infty<x,x<\infty}}$	arctan(sinh(x)) = arccot(csch(x))	ArcTan[Sinh[x]] == ArcCot[Csch[x]]	Failure	Successful	Successful [Tested: 3]	Successful [Tested: 3]
4.23.E41	${\displaystyle{\displaystyle{\operatorname{gd}^{-1}}\left(x\right)=\int_{0}^{x% }\sec t\mathrm{d}t}}$ `\aGudermannian@{x} = \int_{0}^{x}\sec@@{t}\diff{t}`	${\displaystyle{\displaystyle-\frac{1}{2}\pi<x,x<\frac{1}{2}\pi}}$	arctanh(sin(x)) = int(sec(t), t = 0..x)	InverseGudermannian[x] == Integrate[Sec[t], {t, 0, x}, GenerateConditions->None]	Failure	Aborted	Successful [Tested: 2]	Successful [Tested: 2]
4.23.E42	${\displaystyle{\displaystyle{\operatorname{gd}^{-1}}\left(x\right)=\ln\tan% \left(\tfrac{1}{2}x+\tfrac{1}{4}\pi\right)}}$ `\aGudermannian@{x} = \ln@@{\tan@{\tfrac{1}{2}x+\tfrac{1}{4}\pi}}`	${\displaystyle{\displaystyle-\frac{1}{2}\pi<x,x<\frac{1}{2}\pi}}$	arctanh(sin(x)) = ln(tan((1)/(2)x +(1)/(4)Pi))	InverseGudermannian[x] == Log[Tan[Divide[1,2]x +Divide[1,4]Pi]]	Failure	Successful	Successful [Tested: 2]	Successful [Tested: 2]
4.23.E42	${\displaystyle{\displaystyle\ln\tan\left(\tfrac{1}{2}x+\tfrac{1}{4}\pi\right)=% \ln\left(\sec x+\tan x\right)}}$ `\ln@@{\tan@{\tfrac{1}{2}x+\tfrac{1}{4}\pi}} = \ln@{\sec@@{x}+\tan@@{x}}`	${\displaystyle{\displaystyle-\frac{1}{2}\pi<x,x<\frac{1}{2}\pi}}$	ln(tan((1)/(2)x +(1)/(4)Pi)) = ln(sec(x)+ tan(x))	Log[Tan[Divide[1,2]x +Divide[1,4]Pi]] == Log[Sec[x]+ Tan[x]]	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 2]
4.23.E42	${\displaystyle{\displaystyle\ln\left(\sec x+\tan x\right)=\operatorname{% arcsinh}\left(\tan x\right)}}$ `\ln@{\sec@@{x}+\tan@@{x}} = \asinh@{\tan@@{x}}`	${\displaystyle{\displaystyle-\frac{1}{2}\pi<x,x<\frac{1}{2}\pi}}$	ln(sec(x)+ tan(x)) = arcsinh(tan(x))	Log[Sec[x]+ Tan[x]] == ArcSinh[Tan[x]]	Failure	Failure	Successful [Tested: 2]	Failed [1 / 3] Result: Complex[3.046904887125347, 3.141592653589793] Test Values: {Rule[x, 2]}
4.23.E42	${\displaystyle{\displaystyle\operatorname{arcsinh}\left(\tan x\right)=% \operatorname{arccsch}\left(\cot x\right)}}$ `\asinh@{\tan@@{x}} = \acsch@{\cot@@{x}}`	${\displaystyle{\displaystyle-\frac{1}{2}\pi<x,x<\frac{1}{2}\pi}}$	arcsinh(tan(x)) = arccsch(cot(x))	ArcSinh[Tan[x]] == ArcCsch[Cot[x]]	Failure	Successful	Successful [Tested: 2]	Successful [Tested: 2]
4.23.E42	${\displaystyle{\displaystyle\operatorname{arccsch}\left(\cot x\right)=% \operatorname{arccosh}\left(\sec x\right)}}$ `\acsch@{\cot@@{x}} = \acosh@{\sec@@{x}}`	${\displaystyle{\displaystyle-\frac{1}{2}\pi<x,x<\frac{1}{2}\pi}}$	arccsch(cot(x)) = arccosh(sec(x))	ArcCsch[Cot[x]] == ArcCosh[Sec[x]]	Failure	Failure	Successful [Tested: 2]	Failed [1 / 3] Result: Complex[-3.046904887125347, -3.141592653589793] Test Values: {Rule[x, 2]}
4.23.E42	${\displaystyle{\displaystyle\operatorname{arccosh}\left(\sec x\right)=% \operatorname{arcsech}\left(\cos x\right)}}$ `\acosh@{\sec@@{x}} = \asech@{\cos@@{x}}`	${\displaystyle{\displaystyle-\frac{1}{2}\pi<x,x<\frac{1}{2}\pi}}$	arccosh(sec(x)) = arcsech(cos(x))	ArcCosh[Sec[x]] == ArcSech[Cos[x]]	Failure	Successful	Successful [Tested: 2]	Successful [Tested: 2]
4.23.E42	${\displaystyle{\displaystyle\operatorname{arcsech}\left(\cos x\right)=% \operatorname{arctanh}\left(\sin x\right)}}$ `\asech@{\cos@@{x}} = \atanh@{\sin@@{x}}`	${\displaystyle{\displaystyle-\frac{1}{2}\pi<x,x<\frac{1}{2}\pi}}$	arcsech(cos(x)) = arctanh(sin(x))	ArcSech[Cos[x]] == ArcTanh[Sin[x]]	Failure	Failure	Successful [Tested: 2]	Failed [1 / 3] Result: Complex[0.0, 3.141592653589793] Test Values: {Rule[x, 2]}
4.23.E42	${\displaystyle{\displaystyle\operatorname{arctanh}\left(\sin x\right)=% \operatorname{arccoth}\left(\csc x\right)}}$ `\atanh@{\sin@@{x}} = \acoth@{\csc@@{x}}`	${\displaystyle{\displaystyle-\frac{1}{2}\pi<x,x<\frac{1}{2}\pi}}$	arctanh(sin(x)) = arccoth(csc(x))	ArcTanh[Sin[x]] == ArcCoth[Csc[x]]	Failure	Successful	Successful [Tested: 2]	Successful [Tested: 2]

@@ Line 14: / Line 14: @@
 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
 |-
-| [https://dlmf.nist.gov/4.23.E1 4.23.E1] || [[Item:Q1753|<math>\Asin@@{z} = \int_{0}^{z}\frac{\diff{t}}{(1-t^{2})^{1/2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Asin@@{z} = \int_{0}^{z}\frac{\diff{t}}{(1-t^{2})^{1/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[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/4.23.E1 4.23.E1] || <math qid="Q1753">\Asin@@{z} = \int_{0}^{z}\frac{\diff{t}}{(1-t^{2})^{1/2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Asin@@{z} = \int_{0}^{z}\frac{\diff{t}}{(1-t^{2})^{1/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[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/4.23.E2 4.23.E2] || [[Item:Q1754|<math>\Acos@@{z} = \int_{z}^{1}\frac{\diff{t}}{(1-t^{2})^{1/2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acos@@{z} = \int_{z}^{1}\frac{\diff{t}}{(1-t^{2})^{1/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[z] == Integrate[Divide[1,(1 - (t)^(2))^(1/2)], {t, z, 1}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.23.E2 4.23.E2] || <math qid="Q1754">\Acos@@{z} = \int_{z}^{1}\frac{\diff{t}}{(1-t^{2})^{1/2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acos@@{z} = \int_{z}^{1}\frac{\diff{t}}{(1-t^{2})^{1/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[z] == Integrate[Divide[1,(1 - (t)^(2))^(1/2)], {t, z, 1}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.23.E3 4.23.E3] || [[Item:Q1755|<math>\Atan@@{z} = \int_{0}^{z}\frac{\diff{t}}{1+t^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Atan@@{z} = \int_{0}^{z}\frac{\diff{t}}{1+t^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[z] == Integrate[Divide[1,1 + (t)^(2)], {t, 0, z}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 1]
+| [https://dlmf.nist.gov/4.23.E3 4.23.E3] || <math qid="Q1755">\Atan@@{z} = \int_{0}^{z}\frac{\diff{t}}{1+t^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Atan@@{z} = \int_{0}^{z}\frac{\diff{t}}{1+t^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[z] == Integrate[Divide[1,1 + (t)^(2)], {t, 0, z}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.23.E4 4.23.E4] || [[Item:Q1756|<math>\Acsc@@{z} = \Asin@{1/z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acsc@@{z} = \Asin@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCsc[z] == ArcSin[1/z]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.23.E4 4.23.E4] || <math qid="Q1756">\Acsc@@{z} = \Asin@{1/z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acsc@@{z} = \Asin@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCsc[z] == ArcSin[1/z]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.23.E5 4.23.E5] || [[Item:Q1757|<math>\Asec@@{z} = \Acos@{1/z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Asec@@{z} = \Acos@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSec[z] == ArcCos[1/z]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.23.E5 4.23.E5] || <math qid="Q1757">\Asec@@{z} = \Acos@{1/z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Asec@@{z} = \Acos@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSec[z] == ArcCos[1/z]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.23.E6 4.23.E6] || [[Item:Q1758|<math>\Acot@@{z} = \Atan@{1/z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acot@@{z} = \Atan@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCot[z] == ArcTan[1/z]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.23.E6 4.23.E6] || <math qid="Q1758">\Acot@@{z} = \Atan@{1/z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acot@@{z} = \Atan@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCot[z] == ArcTan[1/z]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.23.E7 4.23.E7] || [[Item:Q1759|<math>\acsc@@{z} = \asin@{1/z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acsc@@{z} = \asin@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccsc(z) = arcsin(1/z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCsc[z] == ArcSin[1/z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.23.E7 4.23.E7] || <math qid="Q1759">\acsc@@{z} = \asin@{1/z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acsc@@{z} = \asin@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccsc(z) = arcsin(1/z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCsc[z] == ArcSin[1/z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.23.E8 4.23.E8] || [[Item:Q1760|<math>\asec@@{z} = \acos@{1/z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asec@@{z} = \acos@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsec(z) = arccos(1/z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSec[z] == ArcCos[1/z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.23.E8 4.23.E8] || <math qid="Q1760">\asec@@{z} = \acos@{1/z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asec@@{z} = \acos@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsec(z) = arccos(1/z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSec[z] == ArcCos[1/z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.23.E9 4.23.E9] || [[Item:Q1761|<math>\acot@@{z} = \atan@{1/z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acot@@{z} = \atan@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccot(z) = arctan(1/z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCot[z] == ArcTan[1/z]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.141592654+0.*I
+| [https://dlmf.nist.gov/4.23.E9 4.23.E9] || <math qid="Q1761">\acot@@{z} = \atan@{1/z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acot@@{z} = \atan@{1/z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccot(z) = arctan(1/z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCot[z] == ArcTan[1/z]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.141592654+0.*I
 Test Values: {z = -1/2+1/2*I*3^(1/2), z = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.141592654+0.*I
 Test Values: {z = -1/2*3^(1/2)-1/2*I, z = 1/2}</syntaxhighlight><br></div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.23.E10 4.23.E10] || [[Item:Q1762|<math>\asin@{-z} = -\asin@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@{-z} = -\asin@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsin(- z) = - arcsin(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[- z] == - ArcSin[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.23.E10 4.23.E10] || <math qid="Q1762">\asin@{-z} = -\asin@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@{-z} = -\asin@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsin(- z) = - arcsin(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[- z] == - ArcSin[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.23.E11 4.23.E11] || [[Item:Q1763|<math>\acos@{-z} = \pi-\acos@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@{-z} = \pi-\acos@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(- z) = Pi - arccos(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[- z] == Pi - ArcCos[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.23.E11 4.23.E11] || <math qid="Q1763">\acos@{-z} = \pi-\acos@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@{-z} = \pi-\acos@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(- z) = Pi - arccos(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[- z] == Pi - ArcCos[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.23.E12 4.23.E12] || [[Item:Q1764|<math>\atan@{-z} = -\atan@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atan@{-z} = -\atan@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctan(- z) = - arctan(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[- z] == - ArcTan[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
+| [https://dlmf.nist.gov/4.23.E12 4.23.E12] || <math qid="Q1764">\atan@{-z} = -\atan@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atan@{-z} = -\atan@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctan(- z) = - arctan(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[- z] == - ArcTan[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.23.E13 4.23.E13] || [[Item:Q1765|<math>\acsc@{-z} = -\acsc@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acsc@{-z} = -\acsc@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccsc(- z) = - arccsc(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCsc[- z] == - ArcCsc[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.23.E13 4.23.E13] || <math qid="Q1765">\acsc@{-z} = -\acsc@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acsc@{-z} = -\acsc@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccsc(- z) = - arccsc(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCsc[- z] == - ArcCsc[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.23.E14 4.23.E14] || [[Item:Q1766|<math>\asec@{-z} = \pi-\asec@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asec@{-z} = \pi-\asec@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsec(- z) = Pi - arcsec(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSec[- z] == Pi - ArcSec[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.23.E14 4.23.E14] || <math qid="Q1766">\asec@{-z} = \pi-\asec@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asec@{-z} = \pi-\asec@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsec(- z) = Pi - arcsec(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSec[- z] == Pi - ArcSec[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.23.E15 4.23.E15] || [[Item:Q1767|<math>\acot@{-z} = -\acot@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acot@{-z} = -\acot@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccot(- z) = - arccot(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCot[- z] == - ArcCot[z]</syntaxhighlight> || Failure || Successful || Skip - No test values generated || Successful [Tested: 1]
+| [https://dlmf.nist.gov/4.23.E15 4.23.E15] || <math qid="Q1767">\acot@{-z} = -\acot@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acot@{-z} = -\acot@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccot(- z) = - arccot(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCot[- z] == - ArcCot[z]</syntaxhighlight> || Failure || Successful || Skip - No test values generated || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.23.E16 4.23.E16] || [[Item:Q1768|<math>\acos@@{z} = \tfrac{1}{2}\pi-\asin@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{z} = \tfrac{1}{2}\pi-\asin@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(z) = (1)/(2)*Pi - arcsin(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[z] == Divide[1,2]*Pi - ArcSin[z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.23.E16 4.23.E16] || <math qid="Q1768">\acos@@{z} = \tfrac{1}{2}\pi-\asin@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{z} = \tfrac{1}{2}\pi-\asin@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(z) = (1)/(2)*Pi - arcsin(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[z] == Divide[1,2]*Pi - ArcSin[z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.23.E17 4.23.E17] || [[Item:Q1769|<math>\asec@@{z} = \tfrac{1}{2}\pi-\acsc@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asec@@{z} = \tfrac{1}{2}\pi-\acsc@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsec(z) = (1)/(2)*Pi - arccsc(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSec[z] == Divide[1,2]*Pi - ArcCsc[z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.23.E17 4.23.E17] || <math qid="Q1769">\asec@@{z} = \tfrac{1}{2}\pi-\acsc@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asec@@{z} = \tfrac{1}{2}\pi-\acsc@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsec(z) = (1)/(2)*Pi - arccsc(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSec[z] == Divide[1,2]*Pi - ArcCsc[z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.23.E18 4.23.E18] || [[Item:Q1770|<math>\acot@@{z} = +\tfrac{1}{2}\pi-\atan@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acot@@{z} = +\tfrac{1}{2}\pi-\atan@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccot(z) = +(1)/(2)*Pi - arctan(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCot[z] == +Divide[1,2]*Pi - ArcTan[z]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 1]
+| [https://dlmf.nist.gov/4.23.E18 4.23.E18] || <math qid="Q1770">\acot@@{z} = +\tfrac{1}{2}\pi-\atan@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acot@@{z} = +\tfrac{1}{2}\pi-\atan@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccot(z) = +(1)/(2)*Pi - arctan(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCot[z] == +Divide[1,2]*Pi - ArcTan[z]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.23.E18 4.23.E18] || [[Item:Q1770|<math>\acot@@{z} = -\tfrac{1}{2}\pi-\atan@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acot@@{z} = -\tfrac{1}{2}\pi-\atan@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccot(z) = -(1)/(2)*Pi - arctan(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCot[z] == -Divide[1,2]*Pi - ArcTan[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.141592654+0.*I
+| [https://dlmf.nist.gov/4.23.E18 4.23.E18] || <math qid="Q1770">\acot@@{z} = -\tfrac{1}{2}\pi-\atan@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acot@@{z} = -\tfrac{1}{2}\pi-\atan@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccot(z) = -(1)/(2)*Pi - arctan(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCot[z] == -Divide[1,2]*Pi - ArcTan[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.141592654+0.*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, z = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.141592654+0.*I
 Test Values: {z = -1/2+1/2*I*3^(1/2), z = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.141592654+0.*I
@@ Line 59: / Line 59: @@
 Test Values: {Rule[z, Rational[1, 2]]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.23.E19 4.23.E19] || [[Item:Q1771|<math>\asin@@{z} = -i\ln@{(1-z^{2})^{1/2}+iz}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@@{z} = -i\ln@{(1-z^{2})^{1/2}+iz}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsin(z) = - I*ln((1 - (z)^(2))^(1/2)+ I*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[z] == - I*Log[(1 - (z)^(2))^(1/2)+ I*z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.23.E19 4.23.E19] || <math qid="Q1771">\asin@@{z} = -i\ln@{(1-z^{2})^{1/2}+iz}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@@{z} = -i\ln@{(1-z^{2})^{1/2}+iz}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsin(z) = - I*ln((1 - (z)^(2))^(1/2)+ I*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[z] == - I*Log[(1 - (z)^(2))^(1/2)+ I*z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.23.E20 4.23.E20] || [[Item:Q1772|<math>\asin@@{x} = \tfrac{1}{2}\pi+ i\ln@{(x^{2}-1)^{1/2}+x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@@{x} = \tfrac{1}{2}\pi+ i\ln@{(x^{2}-1)^{1/2}+x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsin(x) = (1)/(2)*Pi + I*ln(((x)^(2)- 1)^(1/2)+ x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[x] == Divide[1,2]*Pi + I*Log[((x)^(2)- 1)^(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: 0.-1.924847300*I
+| [https://dlmf.nist.gov/4.23.E20 4.23.E20] || <math qid="Q1772">\asin@@{x} = \tfrac{1}{2}\pi+ i\ln@{(x^{2}-1)^{1/2}+x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@@{x} = \tfrac{1}{2}\pi+ i\ln@{(x^{2}-1)^{1/2}+x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsin(x) = (1)/(2)*Pi + I*ln(((x)^(2)- 1)^(1/2)+ x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[x] == Divide[1,2]*Pi + I*Log[((x)^(2)- 1)^(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: 0.-1.924847300*I
 Test Values: {x = 1.5, x = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0.-2.633915794*I
 Test Values: {x = 2, x = 3/2}</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, -1.9248473002384139]
 Test Values: {Rule[x, Rational[3, 2]]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.23.E20 4.23.E20] || [[Item:Q1772|<math>\asin@@{x} = \tfrac{1}{2}\pi- i\ln@{(x^{2}-1)^{1/2}+x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@@{x} = \tfrac{1}{2}\pi- i\ln@{(x^{2}-1)^{1/2}+x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsin(x) = (1)/(2)*Pi - I*ln(((x)^(2)- 1)^(1/2)+ x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[x] == Divide[1,2]*Pi - I*Log[((x)^(2)- 1)^(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: -2.094395102+.1347500000e-10*I
+| [https://dlmf.nist.gov/4.23.E20 4.23.E20] || <math qid="Q1772">\asin@@{x} = \tfrac{1}{2}\pi- i\ln@{(x^{2}-1)^{1/2}+x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@@{x} = \tfrac{1}{2}\pi- i\ln@{(x^{2}-1)^{1/2}+x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsin(x) = (1)/(2)*Pi - I*ln(((x)^(2)- 1)^(1/2)+ x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[x] == Divide[1,2]*Pi - I*Log[((x)^(2)- 1)^(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: -2.094395102+.1347500000e-10*I
 Test Values: {x = .5, x = 3/2}</syntaxhighlight><br></div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.23.E21 4.23.E21] || [[Item:Q1773|<math>\asin@@{x} = -\tfrac{1}{2}\pi+ i\ln@{(x^{2}-1)^{1/2}-x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@@{x} = -\tfrac{1}{2}\pi+ i\ln@{(x^{2}-1)^{1/2}-x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsin(x) = -(1)/(2)*Pi + I*ln(((x)^(2)- 1)^(1/2)- x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[x] == -Divide[1,2]*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: 6.283185308+.7e-9*I
+| [https://dlmf.nist.gov/4.23.E21 4.23.E21] || <math qid="Q1773">\asin@@{x} = -\tfrac{1}{2}\pi+ i\ln@{(x^{2}-1)^{1/2}-x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@@{x} = -\tfrac{1}{2}\pi+ i\ln@{(x^{2}-1)^{1/2}-x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsin(x) = -(1)/(2)*Pi + I*ln(((x)^(2)- 1)^(1/2)- x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[x] == -Divide[1,2]*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: 6.283185308+.7e-9*I
 Test Values: {x = 1.5, x = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 4.188790205-.1347500000e-10*I
 Test Values: {x = .5, x = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 6.283185308+.2e-8*I
 Test Values: {x = 2, x = -2}</syntaxhighlight><br></div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.23.E21 4.23.E21] || [[Item:Q1773|<math>\asin@@{x} = -\tfrac{1}{2}\pi- i\ln@{(x^{2}-1)^{1/2}-x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@@{x} = -\tfrac{1}{2}\pi- i\ln@{(x^{2}-1)^{1/2}-x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsin(x) = -(1)/(2)*Pi - I*ln(((x)^(2)- 1)^(1/2)- x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[x] == -Divide[1,2]*Pi - I*Log[((x)^(2)- 1)^(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: 0.-1.924847301*I
+| [https://dlmf.nist.gov/4.23.E21 4.23.E21] || <math qid="Q1773">\asin@@{x} = -\tfrac{1}{2}\pi- i\ln@{(x^{2}-1)^{1/2}-x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@@{x} = -\tfrac{1}{2}\pi- i\ln@{(x^{2}-1)^{1/2}-x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsin(x) = -(1)/(2)*Pi - I*ln(((x)^(2)- 1)^(1/2)- x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[x] == -Divide[1,2]*Pi - I*Log[((x)^(2)- 1)^(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: 0.-1.924847301*I
 Test Values: {x = 1.5, x = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0.-2.633915796*I
 Test Values: {x = 2, x = -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, 2.633915793849633]
 Test Values: {Rule[x, -2]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.23.E22 4.23.E22] || [[Item:Q1774|<math>\acos@@{z} = \tfrac{1}{2}\pi+i\ln@{(1-z^{2})^{1/2}+iz}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{z} = \tfrac{1}{2}\pi+i\ln@{(1-z^{2})^{1/2}+iz}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(z) = (1)/(2)*Pi + I*ln((1 - (z)^(2))^(1/2)+ I*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[z] == Divide[1,2]*Pi + I*Log[(1 - (z)^(2))^(1/2)+ I*z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.23.E22 4.23.E22] || <math qid="Q1774">\acos@@{z} = \tfrac{1}{2}\pi+i\ln@{(1-z^{2})^{1/2}+iz}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{z} = \tfrac{1}{2}\pi+i\ln@{(1-z^{2})^{1/2}+iz}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(z) = (1)/(2)*Pi + I*ln((1 - (z)^(2))^(1/2)+ I*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[z] == Divide[1,2]*Pi + I*Log[(1 - (z)^(2))^(1/2)+ I*z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.23.E23 4.23.E23] || [[Item:Q1775|<math>\acos@@{z} = -2i\ln@{\left(\frac{1+z}{2}\right)^{1/2}+i\left(\frac{1-z}{2}\right)^{1/2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{z} = -2i\ln@{\left(\frac{1+z}{2}\right)^{1/2}+i\left(\frac{1-z}{2}\right)^{1/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(z) = - 2*I*ln(((1 + z)/(2))^(1/2)+ I*((1 - z)/(2))^(1/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[z] == - 2*I*Log[(Divide[1 + z,2])^(1/2)+ I*(Divide[1 - z,2])^(1/2)]</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.23.E23 4.23.E23] || <math qid="Q1775">\acos@@{z} = -2i\ln@{\left(\frac{1+z}{2}\right)^{1/2}+i\left(\frac{1-z}{2}\right)^{1/2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{z} = -2i\ln@{\left(\frac{1+z}{2}\right)^{1/2}+i\left(\frac{1-z}{2}\right)^{1/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(z) = - 2*I*ln(((1 + z)/(2))^(1/2)+ I*((1 - z)/(2))^(1/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[z] == - 2*I*Log[(Divide[1 + z,2])^(1/2)+ I*(Divide[1 - z,2])^(1/2)]</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.23.E24 4.23.E24] || [[Item:Q1776|<math>\acos@@{x} = - i\ln@{(x^{2}-1)^{1/2}+x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{x} = - i\ln@{(x^{2}-1)^{1/2}+x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(x) = - I*ln(((x)^(2)- 1)^(1/2)+ x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[x] == - I*Log[((x)^(2)- 1)^(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: 1.924847300*I
+| [https://dlmf.nist.gov/4.23.E24 4.23.E24] || <math qid="Q1776">\acos@@{x} = - i\ln@{(x^{2}-1)^{1/2}+x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{x} = - i\ln@{(x^{2}-1)^{1/2}+x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(x) = - I*ln(((x)^(2)- 1)^(1/2)+ x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[x] == - I*Log[((x)^(2)- 1)^(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: 1.924847300*I
 Test Values: {x = 1.5, x = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.633915794*I
 Test Values: {x = 2, x = 3/2}</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, 1.9248473002384139]
 Test Values: {Rule[x, Rational[3, 2]]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.23.E24 4.23.E24] || [[Item:Q1776|<math>\acos@@{x} = + i\ln@{(x^{2}-1)^{1/2}+x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{x} = + i\ln@{(x^{2}-1)^{1/2}+x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(x) = + I*ln(((x)^(2)- 1)^(1/2)+ x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[x] == + I*Log[((x)^(2)- 1)^(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: 2.094395102-.1347500000e-10*I
+| [https://dlmf.nist.gov/4.23.E24 4.23.E24] || <math qid="Q1776">\acos@@{x} = + i\ln@{(x^{2}-1)^{1/2}+x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{x} = + i\ln@{(x^{2}-1)^{1/2}+x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(x) = + I*ln(((x)^(2)- 1)^(1/2)+ x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[x] == + I*Log[((x)^(2)- 1)^(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: 2.094395102-.1347500000e-10*I
 Test Values: {x = .5, x = 3/2}</syntaxhighlight><br></div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.23.E25 4.23.E25] || [[Item:Q1777|<math>\acos@@{x} = \pi- i\ln@{(x^{2}-1)^{1/2}-x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{x} = \pi- i\ln@{(x^{2}-1)^{1/2}-x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(x) = Pi - I*ln(((x)^(2)- 1)^(1/2)- x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[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: -6.283185308-.7e-9*I
+| [https://dlmf.nist.gov/4.23.E25 4.23.E25] || <math qid="Q1777">\acos@@{x} = \pi- i\ln@{(x^{2}-1)^{1/2}-x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{x} = \pi- i\ln@{(x^{2}-1)^{1/2}-x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(x) = Pi - I*ln(((x)^(2)- 1)^(1/2)- x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[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: -6.283185308-.7e-9*I
 Test Values: {x = 1.5, x = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -4.188790205+.1347500000e-10*I
 Test Values: {x = .5, x = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -6.283185308-.2e-8*I
 Test Values: {x = 2, x = -2}</syntaxhighlight><br></div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.23.E25 4.23.E25] || [[Item:Q1777|<math>\acos@@{x} = \pi+ i\ln@{(x^{2}-1)^{1/2}-x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{x} = \pi+ i\ln@{(x^{2}-1)^{1/2}-x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(x) = Pi + I*ln(((x)^(2)- 1)^(1/2)- x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[x] == Pi + I*Log[((x)^(2)- 1)^(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: 0.+1.924847301*I
+| [https://dlmf.nist.gov/4.23.E25 4.23.E25] || <math qid="Q1777">\acos@@{x} = \pi+ i\ln@{(x^{2}-1)^{1/2}-x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{x} = \pi+ i\ln@{(x^{2}-1)^{1/2}-x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(x) = Pi + I*ln(((x)^(2)- 1)^(1/2)- x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[x] == Pi + I*Log[((x)^(2)- 1)^(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: 0.+1.924847301*I
 Test Values: {x = 1.5, x = -2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0.+2.633915796*I
 Test Values: {x = 2, x = -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, -2.633915793849633]
 Test Values: {Rule[x, -2]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.23.E26 4.23.E26] || [[Item:Q1778|<math>\atan@@{z} = \frac{i}{2}\ln@{\frac{i+z}{i-z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atan@@{z} = \frac{i}{2}\ln@{\frac{i+z}{i-z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctan(z) = (I)/(2)*ln((I + z)/(I - z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[z] == Divide[I,2]*Log[Divide[I + z,I - z]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.23.E26 4.23.E26] || <math qid="Q1778">\atan@@{z} = \frac{i}{2}\ln@{\frac{i+z}{i-z}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atan@@{z} = \frac{i}{2}\ln@{\frac{i+z}{i-z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctan(z) = (I)/(2)*ln((I + z)/(I - z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[z] == Divide[I,2]*Log[Divide[I + z,I - z]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.23.E27 4.23.E27] || [[Item:Q1779|<math>\atan@{iy} = +\frac{1}{2}\pi+\frac{i}{2}\ln@{\frac{y+1}{y-1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atan@{iy} = +\frac{1}{2}\pi+\frac{i}{2}\ln@{\frac{y+1}{y-1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctan(I*y) = +(1)/(2)*Pi +(I)/(2)*ln((y + 1)/(y - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[I*y] == +Divide[1,2]*Pi +Divide[I,2]*Log[Divide[y + 1,y - 1]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.141592654-.2e-9*I
+| [https://dlmf.nist.gov/4.23.E27 4.23.E27] || <math qid="Q1779">\atan@{iy} = +\frac{1}{2}\pi+\frac{i}{2}\ln@{\frac{y+1}{y-1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atan@{iy} = +\frac{1}{2}\pi+\frac{i}{2}\ln@{\frac{y+1}{y-1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctan(I*y) = +(1)/(2)*Pi +(I)/(2)*ln((y + 1)/(y - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[I*y] == +Divide[1,2]*Pi +Divide[I,2]*Log[Divide[y + 1,y - 1]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.141592654-.2e-9*I
 Test Values: {y = -1.5, y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -3.141592654+.2e-9*I
 Test Values: {y = -2, y = -3/2}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-3.141592653589793, -1.1102230246251565*^-16]
 Test Values: {Rule[y, Rational[-3, 2]]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.23.E27 4.23.E27] || [[Item:Q1779|<math>\atan@{iy} = -\frac{1}{2}\pi+\frac{i}{2}\ln@{\frac{y+1}{y-1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atan@{iy} = -\frac{1}{2}\pi+\frac{i}{2}\ln@{\frac{y+1}{y-1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctan(I*y) = -(1)/(2)*Pi +(I)/(2)*ln((y + 1)/(y - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[I*y] == -Divide[1,2]*Pi +Divide[I,2]*Log[Divide[y + 1,y - 1]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.141592654+.2e-9*I
+| [https://dlmf.nist.gov/4.23.E27 4.23.E27] || <math qid="Q1779">\atan@{iy} = -\frac{1}{2}\pi+\frac{i}{2}\ln@{\frac{y+1}{y-1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atan@{iy} = -\frac{1}{2}\pi+\frac{i}{2}\ln@{\frac{y+1}{y-1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctan(I*y) = -(1)/(2)*Pi +(I)/(2)*ln((y + 1)/(y - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[I*y] == -Divide[1,2]*Pi +Divide[I,2]*Log[Divide[y + 1,y - 1]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.141592654+.2e-9*I
 Test Values: {y = 1.5, y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.141592654+.2e-9*I
 Test Values: {y = -.5, y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.141592654-.2e-9*I
@@ Line 114: / Line 114: @@
 Test Values: {y = 2, y = -3/2}</syntaxhighlight><br></div></div> || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/4.23.E28 4.23.E28] || [[Item:Q1780|<math>z = \sin@@{w}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \sin@@{w}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = sin(w)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == Sin[w]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .70450695e-2+.1624035369*I
+| [https://dlmf.nist.gov/4.23.E28 4.23.E28] || <math qid="Q1780">z = \sin@@{w}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \sin@@{w}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = sin(w)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == Sin[w]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .70450695e-2+.1624035369*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: -1.358980334+.5284289409*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: -.3589803345-1.203621867*I
@@ Line 122: / Line 122: @@
 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/4.23.E29 4.23.E29] || [[Item:Q1781|<math>z = \cos@@{w}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \cos@@{w}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = cos(w)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == Cos[w]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1354823851+.8969495503*I
+| [https://dlmf.nist.gov/4.23.E29 4.23.E29] || <math qid="Q1781">z = \cos@@{w}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \cos@@{w}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = cos(w)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == Cos[w]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1354823851+.8969495503*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: -1.230543019+1.262974954*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: -.2305430189-.4690758537*I
@@ Line 130: / Line 130: @@
 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/4.23.E30 4.23.E30] || [[Item:Q1782|<math>z = \tan@@{w}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \tan@@{w}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = tan(w)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == Tan[w]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1520945236-.3500402975*I
+| [https://dlmf.nist.gov/4.23.E30 4.23.E30] || <math qid="Q1782">z = \tan@@{w}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \tan@@{w}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = tan(w)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == Tan[w]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1520945236-.3500402975*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: -1.213930880+.159851065e-1*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: -.2139308804-1.716065702*I
@@ Line 138: / Line 138: @@
 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/4.23.E31 4.23.E31] || [[Item:Q1783|<math>w = \Asin@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \Asin@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == ArcSin[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[0.0806272403869902, -0.15847894846240845]
+| [https://dlmf.nist.gov/4.23.E31 4.23.E31] || <math qid="Q1783">w = \Asin@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \Asin@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == ArcSin[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[0.0806272403869902, -0.15847894846240845]
 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[1.2407598364931787, -0.3314429455293106]
 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/4.23.E31 4.23.E31] || [[Item:Q1783|<math>\Asin@@{z} = (-1)^{k}\asin@@{z}+k\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Asin@@{z} = (-1)^{k}\asin@@{z}+k\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[z] == (- 1)^(k)* ArcSin[z]+ k*Pi</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[-1.5707963267948961, 1.3169578969248168]
+| [https://dlmf.nist.gov/4.23.E31 4.23.E31] || <math qid="Q1783">\Asin@@{z} = (-1)^{k}\asin@@{z}+k\pi</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Asin@@{z} = (-1)^{k}\asin@@{z}+k\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[z] == (- 1)^(k)* ArcSin[z]+ k*Pi</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[-1.5707963267948961, 1.3169578969248168]
 Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -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/4.23.E32 4.23.E32] || [[Item:Q1784|<math>w = \Acos@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \Acos@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == ArcCos[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[0.08062724038699065, 1.1584789484624083]
+| [https://dlmf.nist.gov/4.23.E32 4.23.E32] || <math qid="Q1784">w = \Acos@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \Acos@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == ArcCos[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[0.08062724038699065, 1.1584789484624083]
 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[-1.0795053557191978, 1.3314429455293104]
 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/4.23.E32 4.23.E32] || [[Item:Q1784|<math>\Acos@@{z} = +\acos@@{z}+2k\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acos@@{z} = +\acos@@{z}+2k\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[z] == + ArcCos[z]+ 2*k*Pi</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -6.283185307179586
+| [https://dlmf.nist.gov/4.23.E32 4.23.E32] || <math qid="Q1784">\Acos@@{z} = +\acos@@{z}+2k\pi</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acos@@{z} = +\acos@@{z}+2k\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[z] == + ArcCos[z]+ 2*k*Pi</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -6.283185307179586
 Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -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/4.23.E32 4.23.E32] || [[Item:Q1784|<math>\Acos@@{z} = -\acos@@{z}+2k\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acos@@{z} = -\acos@@{z}+2k\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[z] == - ArcCos[z]+ 2*k*Pi</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[-4.71238898038469, -1.3169578969248168]
+| [https://dlmf.nist.gov/4.23.E32 4.23.E32] || <math qid="Q1784">\Acos@@{z} = -\acos@@{z}+2k\pi</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Acos@@{z} = -\acos@@{z}+2k\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[z] == - ArcCos[z]+ 2*k*Pi</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[-4.71238898038469, -1.3169578969248168]
 Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-10.995574287564276, -1.3169578969248168]
 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/4.23.E33 4.23.E33] || [[Item:Q1785|<math>w = \Atan@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \Atan@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == ArcTan[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[0.4023777947836326, 0.49999999999999994]
+| [https://dlmf.nist.gov/4.23.E33 4.23.E33] || <math qid="Q1785">w = \Atan@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \Atan@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == ArcTan[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[0.4023777947836326, 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[-0.9636476090008059, 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/4.23.E33 4.23.E33] || [[Item:Q1785|<math>\Atan@@{z} = \atan@@{z}+k\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Atan@@{z} = \atan@@{z}+k\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[z] == ArcTan[z]+ k*Pi</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.141592653589793
+| [https://dlmf.nist.gov/4.23.E33 4.23.E33] || <math qid="Q1785">\Atan@@{z} = \atan@@{z}+k\pi</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Atan@@{z} = \atan@@{z}+k\pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[z] == ArcTan[z]+ k*Pi</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.141592653589793
 Test Values: {Rule[k, 1], Rule[z, Rational[1, 2]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -6.283185307179586
 Test Values: {Rule[k, 2], Rule[z, Rational[1, 2]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/4.23.E34 4.23.E34] || [[Item:Q1786|<math>\asin@@{z} = \asin@@{\beta}+\iunit\sign@{y}\ln@{\alpha+(\alpha^{2}-1)^{1/2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@@{z} = \asin@@{\beta}+\iunit\sign@{y}\ln@{\alpha+(\alpha^{2}-1)^{1/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsin(x + y*I) = arcsin((1)/(2)*((x + 1)^(2)+ (y)^(2))^(1/2)-(1)/(2)*((x - 1)^(2)+ (y)^(2))^(1/2))+ I*signum(y)*ln(((1)/(2)*((x + 1)^(2)+ (y)^(2))^(1/2)+(1)/(2)*((x - 1)^(2)+ (y)^(2))^(1/2))+(((1)/(2)*((x + 1)^(2)+ (y)^(2))^(1/2)+(1)/(2)*((x - 1)^(2)+ (y)^(2))^(1/2))^(2)- 1)^(1/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[x + y*I] == ArcSin[Divide[1,2]*((x + 1)^(2)+ (y)^(2))^(1/2)-Divide[1,2]*((x - 1)^(2)+ (y)^(2))^(1/2)]+ I*Sign[y]*Log[(Divide[1,2]*((x + 1)^(2)+ (y)^(2))^(1/2)+Divide[1,2]*((x - 1)^(2)+ (y)^(2))^(1/2))+((Divide[1,2]*((x + 1)^(2)+ (y)^(2))^(1/2)+Divide[1,2]*((x - 1)^(2)+ (y)^(2))^(1/2))^(2)- 1)^(1/2)]</syntaxhighlight> || Failure || Failure || Successful [Tested: 18] || Successful [Tested: 18]
+| [https://dlmf.nist.gov/4.23.E34 4.23.E34] || <math qid="Q1786">\asin@@{z} = \asin@@{\beta}+\iunit\sign@{y}\ln@{\alpha+(\alpha^{2}-1)^{1/2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@@{z} = \asin@@{\beta}+\iunit\sign@{y}\ln@{\alpha+(\alpha^{2}-1)^{1/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arcsin(x + y*I) = arcsin((1)/(2)*((x + 1)^(2)+ (y)^(2))^(1/2)-(1)/(2)*((x - 1)^(2)+ (y)^(2))^(1/2))+ I*signum(y)*ln(((1)/(2)*((x + 1)^(2)+ (y)^(2))^(1/2)+(1)/(2)*((x - 1)^(2)+ (y)^(2))^(1/2))+(((1)/(2)*((x + 1)^(2)+ (y)^(2))^(1/2)+(1)/(2)*((x - 1)^(2)+ (y)^(2))^(1/2))^(2)- 1)^(1/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[x + y*I] == ArcSin[Divide[1,2]*((x + 1)^(2)+ (y)^(2))^(1/2)-Divide[1,2]*((x - 1)^(2)+ (y)^(2))^(1/2)]+ I*Sign[y]*Log[(Divide[1,2]*((x + 1)^(2)+ (y)^(2))^(1/2)+Divide[1,2]*((x - 1)^(2)+ (y)^(2))^(1/2))+((Divide[1,2]*((x + 1)^(2)+ (y)^(2))^(1/2)+Divide[1,2]*((x - 1)^(2)+ (y)^(2))^(1/2))^(2)- 1)^(1/2)]</syntaxhighlight> || Failure || Failure || Successful [Tested: 18] || Successful [Tested: 18]
 |-
-| [https://dlmf.nist.gov/4.23.E35 4.23.E35] || [[Item:Q1787|<math>\acos@@{z} = \acos@@{\beta}-\iunit\sign@{y}\ln@{\alpha+(\alpha^{2}-1)^{1/2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{z} = \acos@@{\beta}-\iunit\sign@{y}\ln@{\alpha+(\alpha^{2}-1)^{1/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(x + y*I) = arccos((1)/(2)*((x + 1)^(2)+ (y)^(2))^(1/2)-(1)/(2)*((x - 1)^(2)+ (y)^(2))^(1/2))- I*signum(y)*ln(((1)/(2)*((x + 1)^(2)+ (y)^(2))^(1/2)+(1)/(2)*((x - 1)^(2)+ (y)^(2))^(1/2))+(((1)/(2)*((x + 1)^(2)+ (y)^(2))^(1/2)+(1)/(2)*((x - 1)^(2)+ (y)^(2))^(1/2))^(2)- 1)^(1/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[x + y*I] == ArcCos[Divide[1,2]*((x + 1)^(2)+ (y)^(2))^(1/2)-Divide[1,2]*((x - 1)^(2)+ (y)^(2))^(1/2)]- I*Sign[y]*Log[(Divide[1,2]*((x + 1)^(2)+ (y)^(2))^(1/2)+Divide[1,2]*((x - 1)^(2)+ (y)^(2))^(1/2))+((Divide[1,2]*((x + 1)^(2)+ (y)^(2))^(1/2)+Divide[1,2]*((x - 1)^(2)+ (y)^(2))^(1/2))^(2)- 1)^(1/2)]</syntaxhighlight> || Failure || Failure || Successful [Tested: 18] || Successful [Tested: 18]
+| [https://dlmf.nist.gov/4.23.E35 4.23.E35] || <math qid="Q1787">\acos@@{z} = \acos@@{\beta}-\iunit\sign@{y}\ln@{\alpha+(\alpha^{2}-1)^{1/2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{z} = \acos@@{\beta}-\iunit\sign@{y}\ln@{\alpha+(\alpha^{2}-1)^{1/2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(x + y*I) = arccos((1)/(2)*((x + 1)^(2)+ (y)^(2))^(1/2)-(1)/(2)*((x - 1)^(2)+ (y)^(2))^(1/2))- I*signum(y)*ln(((1)/(2)*((x + 1)^(2)+ (y)^(2))^(1/2)+(1)/(2)*((x - 1)^(2)+ (y)^(2))^(1/2))+(((1)/(2)*((x + 1)^(2)+ (y)^(2))^(1/2)+(1)/(2)*((x - 1)^(2)+ (y)^(2))^(1/2))^(2)- 1)^(1/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[x + y*I] == ArcCos[Divide[1,2]*((x + 1)^(2)+ (y)^(2))^(1/2)-Divide[1,2]*((x - 1)^(2)+ (y)^(2))^(1/2)]- I*Sign[y]*Log[(Divide[1,2]*((x + 1)^(2)+ (y)^(2))^(1/2)+Divide[1,2]*((x - 1)^(2)+ (y)^(2))^(1/2))+((Divide[1,2]*((x + 1)^(2)+ (y)^(2))^(1/2)+Divide[1,2]*((x - 1)^(2)+ (y)^(2))^(1/2))^(2)- 1)^(1/2)]</syntaxhighlight> || Failure || Failure || Successful [Tested: 18] || Successful [Tested: 18]
 |-
-| [https://dlmf.nist.gov/4.23.E36 4.23.E36] || [[Item:Q1788|<math>\atan@@{z} = \tfrac{1}{2}\atan@{\frac{2x}{1-x^{2}-y^{2}}}+\tfrac{1}{4}i\ln@{\frac{x^{2}+(y+1)^{2}}{x^{2}+(y-1)^{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atan@@{z} = \tfrac{1}{2}\atan@{\frac{2x}{1-x^{2}-y^{2}}}+\tfrac{1}{4}i\ln@{\frac{x^{2}+(y+1)^{2}}{x^{2}+(y-1)^{2}}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctan(x + y*I) = (1)/(2)*arctan((2*x)/(1 - (x)^(2)- (y)^(2)))+(1)/(4)*I*ln(((x)^(2)+(y + 1)^(2))/((x)^(2)+(y - 1)^(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[x + y*I] == Divide[1,2]*ArcTan[Divide[2*x,1 - (x)^(2)- (y)^(2)]]+Divide[1,4]*I*Log[Divide[(x)^(2)+(y + 1)^(2),(x)^(2)+(y - 1)^(2)]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [16 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.570796327-.1e-9*I
+| [https://dlmf.nist.gov/4.23.E36 4.23.E36] || <math qid="Q1788">\atan@@{z} = \tfrac{1}{2}\atan@{\frac{2x}{1-x^{2}-y^{2}}}+\tfrac{1}{4}i\ln@{\frac{x^{2}+(y+1)^{2}}{x^{2}+(y-1)^{2}}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atan@@{z} = \tfrac{1}{2}\atan@{\frac{2x}{1-x^{2}-y^{2}}}+\tfrac{1}{4}i\ln@{\frac{x^{2}+(y+1)^{2}}{x^{2}+(y-1)^{2}}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arctan(x + y*I) = (1)/(2)*arctan((2*x)/(1 - (x)^(2)- (y)^(2)))+(1)/(4)*I*ln(((x)^(2)+(y + 1)^(2))/((x)^(2)+(y - 1)^(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[x + y*I] == Divide[1,2]*ArcTan[Divide[2*x,1 - (x)^(2)- (y)^(2)]]+Divide[1,4]*I*Log[Divide[(x)^(2)+(y + 1)^(2),(x)^(2)+(y - 1)^(2)]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [16 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.570796327-.1e-9*I
 Test Values: {x = 1.5, y = -1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.570796327-.1e-9*I
 Test Values: {x = 1.5, y = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.570796327+0.*I
@@ Line 178: / Line 178: @@
 Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/4.23.E39 4.23.E39] || [[Item:Q1791|<math>\Gudermannian@{x} = \int_{0}^{x}\sech@@{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Gudermannian@{x} = \int_{0}^{x}\sech@@{t}\diff{t}</syntaxhighlight> || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>arctan(sinh(x)) = int(sech(t), t = 0..x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gudermannian[x] == Integrate[Sech[t], {t, 0, x}, GenerateConditions->None]</syntaxhighlight> || Successful || Aborted || - || Successful [Tested: 3]
+| [https://dlmf.nist.gov/4.23.E39 4.23.E39] || <math qid="Q1791">\Gudermannian@{x} = \int_{0}^{x}\sech@@{t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Gudermannian@{x} = \int_{0}^{x}\sech@@{t}\diff{t}</syntaxhighlight> || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>arctan(sinh(x)) = int(sech(t), t = 0..x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gudermannian[x] == Integrate[Sech[t], {t, 0, x}, GenerateConditions->None]</syntaxhighlight> || Successful || Aborted || - || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/4.23.E40 4.23.E40] || [[Item:Q1792|<math>\Gudermannian@{x} = 2\atan@{e^{x}}-\tfrac{1}{2}\pi\\</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Gudermannian@{x} = 2\atan@{e^{x}}-\tfrac{1}{2}\pi\\</syntaxhighlight> || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>arctan(sinh(x)) = 2*arctan(exp(x))-(1)/(2)*Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gudermannian[x] == 2*ArcTan[Exp[x]]-Divide[1,2]*Pi</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
+| [https://dlmf.nist.gov/4.23.E40 4.23.E40] || <math qid="Q1792">\Gudermannian@{x} = 2\atan@{e^{x}}-\tfrac{1}{2}\pi\\</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Gudermannian@{x} = 2\atan@{e^{x}}-\tfrac{1}{2}\pi\\</syntaxhighlight> || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>arctan(sinh(x)) = 2*arctan(exp(x))-(1)/(2)*Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gudermannian[x] == 2*ArcTan[Exp[x]]-Divide[1,2]*Pi</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/4.23.E40 4.23.E40] || [[Item:Q1792|<math>2\atan@{e^{x}}-\tfrac{1}{2}\pi\\ = \asin@{\tanh@@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2\atan@{e^{x}}-\tfrac{1}{2}\pi\\ = \asin@{\tanh@@{x}}</syntaxhighlight> || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>2*arctan(exp(x))-(1)/(2)*Pi = arcsin(tanh(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*ArcTan[Exp[x]]-Divide[1,2]*Pi == ArcSin[Tanh[x]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
+| [https://dlmf.nist.gov/4.23.E40 4.23.E40] || <math qid="Q1792">2\atan@{e^{x}}-\tfrac{1}{2}\pi\\ = \asin@{\tanh@@{x}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2\atan@{e^{x}}-\tfrac{1}{2}\pi\\ = \asin@{\tanh@@{x}}</syntaxhighlight> || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>2*arctan(exp(x))-(1)/(2)*Pi = arcsin(tanh(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*ArcTan[Exp[x]]-Divide[1,2]*Pi == ArcSin[Tanh[x]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/4.23.E40 4.23.E40] || [[Item:Q1792|<math>\asin@{\tanh@@{x}} = \acsc@{\coth@@{x}}\\</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@{\tanh@@{x}} = \acsc@{\coth@@{x}}\\</syntaxhighlight> || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>arcsin(tanh(x)) = arccsc(coth(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[Tanh[x]] == ArcCsc[Coth[x]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
+| [https://dlmf.nist.gov/4.23.E40 4.23.E40] || <math qid="Q1792">\asin@{\tanh@@{x}} = \acsc@{\coth@@{x}}\\</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@{\tanh@@{x}} = \acsc@{\coth@@{x}}\\</syntaxhighlight> || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>arcsin(tanh(x)) = arccsc(coth(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[Tanh[x]] == ArcCsc[Coth[x]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/4.23.E40 4.23.E40] || [[Item:Q1792|<math>\acsc@{\coth@@{x}}\\ = \acos@{\sech@@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acsc@{\coth@@{x}}\\ = \acos@{\sech@@{x}}</syntaxhighlight> || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>arccsc(coth(x)) = arccos(sech(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCsc[Coth[x]] == ArcCos[Sech[x]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
+| [https://dlmf.nist.gov/4.23.E40 4.23.E40] || <math qid="Q1792">\acsc@{\coth@@{x}}\\ = \acos@{\sech@@{x}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acsc@{\coth@@{x}}\\ = \acos@{\sech@@{x}}</syntaxhighlight> || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>arccsc(coth(x)) = arccos(sech(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCsc[Coth[x]] == ArcCos[Sech[x]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/4.23.E40 4.23.E40] || [[Item:Q1792|<math>\acos@{\sech@@{x}} = \asec@{\cosh@@{x}}\\</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@{\sech@@{x}} = \asec@{\cosh@@{x}}\\</syntaxhighlight> || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>arccos(sech(x)) = arcsec(cosh(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[Sech[x]] == ArcSec[Cosh[x]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
+| [https://dlmf.nist.gov/4.23.E40 4.23.E40] || <math qid="Q1792">\acos@{\sech@@{x}} = \asec@{\cosh@@{x}}\\</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@{\sech@@{x}} = \asec@{\cosh@@{x}}\\</syntaxhighlight> || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>arccos(sech(x)) = arcsec(cosh(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[Sech[x]] == ArcSec[Cosh[x]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/4.23.E40 4.23.E40] || [[Item:Q1792|<math>\asec@{\cosh@@{x}}\\ = \atan@{\sinh@@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asec@{\cosh@@{x}}\\ = \atan@{\sinh@@{x}}</syntaxhighlight> || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>arcsec(cosh(x)) = arctan(sinh(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSec[Cosh[x]] == ArcTan[Sinh[x]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
+| [https://dlmf.nist.gov/4.23.E40 4.23.E40] || <math qid="Q1792">\asec@{\cosh@@{x}}\\ = \atan@{\sinh@@{x}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asec@{\cosh@@{x}}\\ = \atan@{\sinh@@{x}}</syntaxhighlight> || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>arcsec(cosh(x)) = arctan(sinh(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSec[Cosh[x]] == ArcTan[Sinh[x]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/4.23.E40 4.23.E40] || [[Item:Q1792|<math>\atan@{\sinh@@{x}} = \acot@{\csch@@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atan@{\sinh@@{x}} = \acot@{\csch@@{x}}</syntaxhighlight> || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>arctan(sinh(x)) = arccot(csch(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[Sinh[x]] == ArcCot[Csch[x]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
+| [https://dlmf.nist.gov/4.23.E40 4.23.E40] || <math qid="Q1792">\atan@{\sinh@@{x}} = \acot@{\csch@@{x}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atan@{\sinh@@{x}} = \acot@{\csch@@{x}}</syntaxhighlight> || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>arctan(sinh(x)) = arccot(csch(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[Sinh[x]] == ArcCot[Csch[x]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/4.23.E41 4.23.E41] || [[Item:Q1793|<math>\aGudermannian@{x} = \int_{0}^{x}\sec@@{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\aGudermannian@{x} = \int_{0}^{x}\sec@@{t}\diff{t}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>arctanh(sin(x)) = int(sec(t), t = 0..x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseGudermannian[x] == Integrate[Sec[t], {t, 0, x}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 2] || Successful [Tested: 2]
+| [https://dlmf.nist.gov/4.23.E41 4.23.E41] || <math qid="Q1793">\aGudermannian@{x} = \int_{0}^{x}\sec@@{t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\aGudermannian@{x} = \int_{0}^{x}\sec@@{t}\diff{t}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>arctanh(sin(x)) = int(sec(t), t = 0..x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseGudermannian[x] == Integrate[Sec[t], {t, 0, x}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 2] || Successful [Tested: 2]
 |-
-| [https://dlmf.nist.gov/4.23.E42 4.23.E42] || [[Item:Q1794|<math>\aGudermannian@{x} = \ln@@{\tan@{\tfrac{1}{2}x+\tfrac{1}{4}\pi}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\aGudermannian@{x} = \ln@@{\tan@{\tfrac{1}{2}x+\tfrac{1}{4}\pi}}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>arctanh(sin(x)) = ln(tan((1)/(2)*x +(1)/(4)*Pi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseGudermannian[x] == Log[Tan[Divide[1,2]*x +Divide[1,4]*Pi]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 2] || Successful [Tested: 2]
+| [https://dlmf.nist.gov/4.23.E42 4.23.E42] || <math qid="Q1794">\aGudermannian@{x} = \ln@@{\tan@{\tfrac{1}{2}x+\tfrac{1}{4}\pi}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\aGudermannian@{x} = \ln@@{\tan@{\tfrac{1}{2}x+\tfrac{1}{4}\pi}}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>arctanh(sin(x)) = ln(tan((1)/(2)*x +(1)/(4)*Pi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseGudermannian[x] == Log[Tan[Divide[1,2]*x +Divide[1,4]*Pi]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 2] || Successful [Tested: 2]
 |-
-| [https://dlmf.nist.gov/4.23.E42 4.23.E42] || [[Item:Q1794|<math>\ln@@{\tan@{\tfrac{1}{2}x+\tfrac{1}{4}\pi}} = \ln@{\sec@@{x}+\tan@@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ln@@{\tan@{\tfrac{1}{2}x+\tfrac{1}{4}\pi}} = \ln@{\sec@@{x}+\tan@@{x}}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>ln(tan((1)/(2)*x +(1)/(4)*Pi)) = ln(sec(x)+ tan(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Log[Tan[Divide[1,2]*x +Divide[1,4]*Pi]] == Log[Sec[x]+ Tan[x]]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 2]
+| [https://dlmf.nist.gov/4.23.E42 4.23.E42] || <math qid="Q1794">\ln@@{\tan@{\tfrac{1}{2}x+\tfrac{1}{4}\pi}} = \ln@{\sec@@{x}+\tan@@{x}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ln@@{\tan@{\tfrac{1}{2}x+\tfrac{1}{4}\pi}} = \ln@{\sec@@{x}+\tan@@{x}}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>ln(tan((1)/(2)*x +(1)/(4)*Pi)) = ln(sec(x)+ tan(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Log[Tan[Divide[1,2]*x +Divide[1,4]*Pi]] == Log[Sec[x]+ Tan[x]]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 2]
 |-
-| [https://dlmf.nist.gov/4.23.E42 4.23.E42] || [[Item:Q1794|<math>\ln@{\sec@@{x}+\tan@@{x}} = \asinh@{\tan@@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ln@{\sec@@{x}+\tan@@{x}} = \asinh@{\tan@@{x}}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>ln(sec(x)+ tan(x)) = arcsinh(tan(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Log[Sec[x]+ Tan[x]] == ArcSinh[Tan[x]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 2] || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[3.046904887125347, 3.141592653589793]
+| [https://dlmf.nist.gov/4.23.E42 4.23.E42] || <math qid="Q1794">\ln@{\sec@@{x}+\tan@@{x}} = \asinh@{\tan@@{x}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ln@{\sec@@{x}+\tan@@{x}} = \asinh@{\tan@@{x}}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>ln(sec(x)+ tan(x)) = arcsinh(tan(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Log[Sec[x]+ Tan[x]] == ArcSinh[Tan[x]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 2] || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[3.046904887125347, 3.141592653589793]
 Test Values: {Rule[x, 2]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.23.E42 4.23.E42] || [[Item:Q1794|<math>\asinh@{\tan@@{x}} = \acsch@{\cot@@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asinh@{\tan@@{x}} = \acsch@{\cot@@{x}}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>arcsinh(tan(x)) = arccsch(cot(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[Tan[x]] == ArcCsch[Cot[x]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 2] || Successful [Tested: 2]
+| [https://dlmf.nist.gov/4.23.E42 4.23.E42] || <math qid="Q1794">\asinh@{\tan@@{x}} = \acsch@{\cot@@{x}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asinh@{\tan@@{x}} = \acsch@{\cot@@{x}}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>arcsinh(tan(x)) = arccsch(cot(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[Tan[x]] == ArcCsch[Cot[x]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 2] || Successful [Tested: 2]
 |-
-| [https://dlmf.nist.gov/4.23.E42 4.23.E42] || [[Item:Q1794|<math>\acsch@{\cot@@{x}} = \acosh@{\sec@@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acsch@{\cot@@{x}} = \acosh@{\sec@@{x}}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>arccsch(cot(x)) = arccosh(sec(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCsch[Cot[x]] == ArcCosh[Sec[x]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 2] || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-3.046904887125347, -3.141592653589793]
+| [https://dlmf.nist.gov/4.23.E42 4.23.E42] || <math qid="Q1794">\acsch@{\cot@@{x}} = \acosh@{\sec@@{x}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acsch@{\cot@@{x}} = \acosh@{\sec@@{x}}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>arccsch(cot(x)) = arccosh(sec(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCsch[Cot[x]] == ArcCosh[Sec[x]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 2] || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-3.046904887125347, -3.141592653589793]
 Test Values: {Rule[x, 2]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.23.E42 4.23.E42] || [[Item:Q1794|<math>\acosh@{\sec@@{x}} = \asech@{\cos@@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@{\sec@@{x}} = \asech@{\cos@@{x}}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>arccosh(sec(x)) = arcsech(cos(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[Sec[x]] == ArcSech[Cos[x]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 2] || Successful [Tested: 2]
+| [https://dlmf.nist.gov/4.23.E42 4.23.E42] || <math qid="Q1794">\acosh@{\sec@@{x}} = \asech@{\cos@@{x}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@{\sec@@{x}} = \asech@{\cos@@{x}}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>arccosh(sec(x)) = arcsech(cos(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[Sec[x]] == ArcSech[Cos[x]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 2] || Successful [Tested: 2]
 |-
-| [https://dlmf.nist.gov/4.23.E42 4.23.E42] || [[Item:Q1794|<math>\asech@{\cos@@{x}} = \atanh@{\sin@@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asech@{\cos@@{x}} = \atanh@{\sin@@{x}}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>arcsech(cos(x)) = arctanh(sin(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSech[Cos[x]] == ArcTanh[Sin[x]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 2] || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, 3.141592653589793]
+| [https://dlmf.nist.gov/4.23.E42 4.23.E42] || <math qid="Q1794">\asech@{\cos@@{x}} = \atanh@{\sin@@{x}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asech@{\cos@@{x}} = \atanh@{\sin@@{x}}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>arcsech(cos(x)) = arctanh(sin(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSech[Cos[x]] == ArcTanh[Sin[x]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 2] || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, 3.141592653589793]
 Test Values: {Rule[x, 2]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/4.23.E42 4.23.E42] || [[Item:Q1794|<math>\atanh@{\sin@@{x}} = \acoth@{\csc@@{x}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atanh@{\sin@@{x}} = \acoth@{\csc@@{x}}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>arctanh(sin(x)) = arccoth(csc(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTanh[Sin[x]] == ArcCoth[Csc[x]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 2] || Successful [Tested: 2]
+| [https://dlmf.nist.gov/4.23.E42 4.23.E42] || <math qid="Q1794">\atanh@{\sin@@{x}} = \acoth@{\csc@@{x}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atanh@{\sin@@{x}} = \acoth@{\csc@@{x}}</syntaxhighlight> || <math>-\frac{1}{2}\pi < x, x < \frac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>arctanh(sin(x)) = arccoth(csc(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTanh[Sin[x]] == ArcCoth[Csc[x]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 2] || Successful [Tested: 2]
 |}
 </div>

4.23: Difference between revisions

Latest revision as of 11:07, 28 June 2021

Navigation menu

Search