4.34: Difference between revisions

Latest revision as of 11:09, 28 June 2021

DLMF	Formula	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
4.34.E1	${\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\sinh z=\cosh z}}$ `\deriv{}{z}\sinh@@{z} = \cosh@@{z}`	diff(sinh(z), z) = cosh(z)	D[Sinh[z], z] == Cosh[z]	Successful	Successful	-	Successful [Tested: 7]
4.34.E2	${\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\cosh z=\sinh z}}$ `\deriv{}{z}\cosh@@{z} = \sinh@@{z}`	diff(cosh(z), z) = sinh(z)	D[Cosh[z], z] == Sinh[z]	Successful	Successful	-	Successful [Tested: 7]
4.34.E3	${\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\tanh z={% \operatorname{sech}^{2}}z}}$ `\deriv{}{z}\tanh@@{z} = \sech^{2}@@{z}`	diff(tanh(z), z) = (sech(z))^(2)	D[Tanh[z], z] == (Sech[z])^(2)	Successful	Successful	-	Successful [Tested: 7]
4.34.E4	${\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{csch}z% =-\operatorname{csch}z\coth z}}$ `\deriv{}{z}\csch@@{z} = -\csch@@{z}\coth@@{z}`	diff(csch(z), z) = - csch(z)*coth(z)	D[Csch[z], z] == - Csch[z]*Coth[z]	Successful	Successful	-	Successful [Tested: 7]
4.34.E5	${\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{sech}z% =-\operatorname{sech}z\tanh z}}$ `\deriv{}{z}\sech@@{z} = -\sech@@{z}\tanh@@{z}`	diff(sech(z), z) = - sech(z)*tanh(z)	D[Sech[z], z] == - Sech[z]*Tanh[z]	Successful	Successful	-	Successful [Tested: 7]
4.34.E6	${\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\coth z=-{% \operatorname{csch}^{2}}z}}$ `\deriv{}{z}\coth@@{z} = -\csch^{2}@@{z}`	diff(coth(z), z) = - (csch(z))^(2)	D[Coth[z], z] == - (Csch[z])^(2)	Successful	Successful	-	Successful [Tested: 7]
4.34.E7	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}-a^{2}w% =0}}$ `\deriv[2]{w}{z}-a^{2}w = 0`	diff(w, [z$(2)])- (a)^(2)* w = 0	D[w, {z, 2}]- (a)^(2)* w == 0	Failure	Failure	Failed [300 / 300] Result: -1.948557159-1.125000000I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -1.948557159-1.125000000I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} Result: -1.948557159-1.125000000I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)} Result: -1.948557159-1.125000000I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-1.948557158514987, -1.1249999999999998] Test Values: {Rule[a, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.948557158514987, -1.1249999999999998] Test Values: {Rule[a, -1.5], 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
4.34.E8	${\displaystyle{\displaystyle\left(\frac{\mathrm{d}w}{\mathrm{d}z}\right)^{2}-a% ^{2}w^{2}=1}}$ `\left(\deriv{w}{z}\right)^{2}-a^{2}w^{2} = 1`	(diff(w, z))^(2)- (a)^(2)* (w)^(2) = 1	(D[w, z])^(2)- (a)^(2)* (w)^(2) == 1	Failure	Failure	Failed [300 / 300] Result: -2.125000001-1.948557159I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -2.125000001-1.948557159I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} Result: -2.125000001-1.948557159I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)} Result: -2.125000001-1.948557159I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-2.125, -1.9485571585149868] Test Values: {Rule[a, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-2.125, -1.9485571585149868] Test Values: {Rule[a, -1.5], 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
4.34.E9	${\displaystyle{\displaystyle\left(\frac{\mathrm{d}w}{\mathrm{d}z}\right)^{2}-a% ^{2}w^{2}=-1}}$ `\left(\deriv{w}{z}\right)^{2}-a^{2}w^{2} = -1`	(diff(w, z))^(2)- (a)^(2)* (w)^(2) = - 1	(D[w, z])^(2)- (a)^(2)* (w)^(2) == - 1	Failure	Failure	Failed [272 / 300] Result: -.125000001-1.948557159I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -.125000001-1.948557159I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} Result: -.125000001-1.948557159I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)} Result: -.125000001-1.948557159I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I} ... skip entries to safe data	Failed [272 / 300] Result: Complex[-0.12500000000000022, -1.9485571585149868] Test Values: {Rule[a, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.12500000000000022, -1.9485571585149868] Test Values: {Rule[a, -1.5], 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
4.34.E10	${\displaystyle{\displaystyle\frac{\mathrm{d}w}{\mathrm{d}z}+a^{2}w^{2}=1}}$ `\deriv{w}{z}+a^{2}w^{2} = 1`	diff(w, z)+ (a)^(2)* (w)^(2) = 1	D[w, z]+ (a)^(2)* (w)^(2) == 1	Failure	Failure	Failed [272 / 300] Result: .125000001+1.948557159I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: .125000001+1.948557159I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} Result: .125000001+1.948557159I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)} Result: .125000001+1.948557159I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I} ... skip entries to safe data	Failed [272 / 300] Result: Complex[0.12500000000000022, 1.9485571585149868] Test Values: {Rule[a, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.12500000000000022, 1.9485571585149868] Test Values: {Rule[a, -1.5], 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
4.34.E11	${\displaystyle{\displaystyle w=A\cosh\left(az\right)+B\sinh\left(az\right)}}$ `w = A\cosh@{az}+B\sinh@{az}`	w = Acosh(az)+ Bsinh(az)	w == ACosh[az]+ BSinh[az]	Failure	Failure	Failed [300 / 300] Result: .6001928989+.561234643I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, a = -1.5, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -.6457530113+1.981963256I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, a = -1.5, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} Result: .9837329493+.425340516e-1I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, a = -1.5, w = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)} Result: -.2074648399-3.005064943I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, a = -1.5, w = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.6001928983405861, 0.5612346426489729] Test Values: {Rule[a, -1.5], Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.645753012062901, 1.9819632558589868] Test Values: {Rule[a, -1.5], Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 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
4.34.E12	${\displaystyle{\displaystyle w=(1/a)\sinh\left(az+c\right)}}$ `w = (1/a)\sinh@{az+c}`	w = (1/a)sinh(az + c)	w == (1/a)Sinh[az + c]	Failure	Failure	Failed [300 / 300] Result: -3.126061208-3.246674013I Test Values: {a = -1.5, c = -1.5, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: .7188715257-.3314459800I Test Values: {a = -1.5, c = -1.5, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} Result: .265391293e-1+3.580357057I Test Values: {a = -1.5, c = -1.5, w = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)} Result: .7673365303+.9636329126I Test Values: {a = -1.5, c = -1.5, w = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-3.126061206522873, -3.246674011194613] Test Values: {Rule[a, -1.5], Rule[c, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.7188715253469982, -0.33144598009263954] Test Values: {Rule[a, -1.5], Rule[c, -1.5], 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
4.34.E13	${\displaystyle{\displaystyle w=(1/a)\cosh\left(az+c\right)}}$ `w = (1/a)\cosh@{az+c}`	w = (1/a)cosh(az + c)	w == (1/a)Cosh[az + c]	Failure	Failure	Failed [300 / 300] Result: 4.887803259+4.219013756I Test Values: {a = -1.5, c = -1.5, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: 1.097709449+1.028092043I Test Values: {a = -1.5, c = -1.5, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} Result: 1.724372908-2.512669644I Test Values: {a = -1.5, c = -1.5, w = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)} Result: 1.363701096+.4080617947I Test Values: {a = -1.5, c = -1.5, w = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I} ... skip entries to safe data	Failed [300 / 300] Result: Complex[4.887803257491119, 4.219013753952423] Test Values: {Rule[a, -1.5], Rule[c, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.0977094487385304, 1.0280920432224616] Test Values: {Rule[a, -1.5], Rule[c, -1.5], 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
4.34.E14	${\displaystyle{\displaystyle w=(1/a)\coth\left(az+c\right)}}$ `w = (1/a)\coth@{az+c}`	w = (1/a)coth(az + c)	w == (1/a)Coth[az + c]	Failure	Failure	Failed [300 / 300] Result: .1990274306+.5049301211I Test Values: {a = -1.5, c = -1.5, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: .4235738270+.6074604561I Test Values: {a = -1.5, c = -1.5, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} Result: .2119596261+.4924838498I Test Values: {a = -1.5, c = -1.5, w = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)} Result: .5938323036-.1576784256I Test Values: {a = -1.5, c = -1.5, w = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.19902743024251868, 0.504930121080845] Test Values: {Rule[a, -1.5], Rule[c, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.423573826800421, 0.6074604562830159] Test Values: {Rule[a, -1.5], Rule[c, -1.5], 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

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 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
 |-
-| [https://dlmf.nist.gov/4.34.E1 4.34.E1] || [[Item:Q1861|<math>\deriv{}{z}\sinh@@{z} = \cosh@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\sinh@@{z} = \cosh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(sinh(z), z) = cosh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Sinh[z], z] == Cosh[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.34.E1 4.34.E1] || <math qid="Q1861">\deriv{}{z}\sinh@@{z} = \cosh@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\sinh@@{z} = \cosh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(sinh(z), z) = cosh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Sinh[z], z] == Cosh[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.34.E2 4.34.E2] || [[Item:Q1862|<math>\deriv{}{z}\cosh@@{z} = \sinh@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\cosh@@{z} = \sinh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(cosh(z), z) = sinh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Cosh[z], z] == Sinh[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.34.E2 4.34.E2] || <math qid="Q1862">\deriv{}{z}\cosh@@{z} = \sinh@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\cosh@@{z} = \sinh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(cosh(z), z) = sinh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Cosh[z], z] == Sinh[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.34.E3 4.34.E3] || [[Item:Q1863|<math>\deriv{}{z}\tanh@@{z} = \sech^{2}@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\tanh@@{z} = \sech^{2}@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(tanh(z), z) = (sech(z))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Tanh[z], z] == (Sech[z])^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.34.E3 4.34.E3] || <math qid="Q1863">\deriv{}{z}\tanh@@{z} = \sech^{2}@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\tanh@@{z} = \sech^{2}@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(tanh(z), z) = (sech(z))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Tanh[z], z] == (Sech[z])^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.34.E4 4.34.E4] || [[Item:Q1864|<math>\deriv{}{z}\csch@@{z} = -\csch@@{z}\coth@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\csch@@{z} = -\csch@@{z}\coth@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(csch(z), z) = - csch(z)*coth(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Csch[z], z] == - Csch[z]*Coth[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.34.E4 4.34.E4] || <math qid="Q1864">\deriv{}{z}\csch@@{z} = -\csch@@{z}\coth@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\csch@@{z} = -\csch@@{z}\coth@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(csch(z), z) = - csch(z)*coth(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Csch[z], z] == - Csch[z]*Coth[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.34.E5 4.34.E5] || [[Item:Q1865|<math>\deriv{}{z}\sech@@{z} = -\sech@@{z}\tanh@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\sech@@{z} = -\sech@@{z}\tanh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(sech(z), z) = - sech(z)*tanh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Sech[z], z] == - Sech[z]*Tanh[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.34.E5 4.34.E5] || <math qid="Q1865">\deriv{}{z}\sech@@{z} = -\sech@@{z}\tanh@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\sech@@{z} = -\sech@@{z}\tanh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(sech(z), z) = - sech(z)*tanh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Sech[z], z] == - Sech[z]*Tanh[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/4.34.E6 4.34.E6] || [[Item:Q1866|<math>\deriv{}{z}\coth@@{z} = -\csch^{2}@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\coth@@{z} = -\csch^{2}@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(coth(z), z) = - (csch(z))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Coth[z], z] == - (Csch[z])^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/4.34.E6 4.34.E6] || <math qid="Q1866">\deriv{}{z}\coth@@{z} = -\csch^{2}@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\coth@@{z} = -\csch^{2}@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(coth(z), z) = - (csch(z))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Coth[z], z] == - (Csch[z])^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
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-| [https://dlmf.nist.gov/4.34.E7 4.34.E7] || [[Item:Q1867|<math>\deriv[2]{w}{z}-a^{2}w = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z}-a^{2}w = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)])- (a)^(2)* w = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}]- (a)^(2)* w == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.948557159-1.125000000*I
+| [https://dlmf.nist.gov/4.34.E7 4.34.E7] || <math qid="Q1867">\deriv[2]{w}{z}-a^{2}w = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z}-a^{2}w = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)])- (a)^(2)* w = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}]- (a)^(2)* w == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.948557159-1.125000000*I
 Test Values: {a = -1.5, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.948557159-1.125000000*I
 Test Values: {a = -1.5, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.948557159-1.125000000*I
@@ Line 34: / Line 34: @@
 Test Values: {Rule[a, -1.5], 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/4.34.E8 4.34.E8] || [[Item:Q1868|<math>\left(\deriv{w}{z}\right)^{2}-a^{2}w^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\left(\deriv{w}{z}\right)^{2}-a^{2}w^{2} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(diff(w, z))^(2)- (a)^(2)* (w)^(2) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[w, z])^(2)- (a)^(2)* (w)^(2) == 1</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.125000001-1.948557159*I
+| [https://dlmf.nist.gov/4.34.E8 4.34.E8] || <math qid="Q1868">\left(\deriv{w}{z}\right)^{2}-a^{2}w^{2} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\left(\deriv{w}{z}\right)^{2}-a^{2}w^{2} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(diff(w, z))^(2)- (a)^(2)* (w)^(2) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[w, z])^(2)- (a)^(2)* (w)^(2) == 1</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.125000001-1.948557159*I
 Test Values: {a = -1.5, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.125000001-1.948557159*I
 Test Values: {a = -1.5, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.125000001-1.948557159*I
@@ Line 42: / Line 42: @@
 Test Values: {Rule[a, -1.5], 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/4.34.E9 4.34.E9] || [[Item:Q1869|<math>\left(\deriv{w}{z}\right)^{2}-a^{2}w^{2} = -1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\left(\deriv{w}{z}\right)^{2}-a^{2}w^{2} = -1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(diff(w, z))^(2)- (a)^(2)* (w)^(2) = - 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[w, z])^(2)- (a)^(2)* (w)^(2) == - 1</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [272 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.125000001-1.948557159*I
+| [https://dlmf.nist.gov/4.34.E9 4.34.E9] || <math qid="Q1869">\left(\deriv{w}{z}\right)^{2}-a^{2}w^{2} = -1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\left(\deriv{w}{z}\right)^{2}-a^{2}w^{2} = -1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(diff(w, z))^(2)- (a)^(2)* (w)^(2) = - 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[w, z])^(2)- (a)^(2)* (w)^(2) == - 1</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [272 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.125000001-1.948557159*I
 Test Values: {a = -1.5, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.125000001-1.948557159*I
 Test Values: {a = -1.5, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.125000001-1.948557159*I
@@ Line 50: / Line 50: @@
 Test Values: {Rule[a, -1.5], 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/4.34.E10 4.34.E10] || [[Item:Q1870|<math>\deriv{w}{z}+a^{2}w^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{w}{z}+a^{2}w^{2} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, z)+ (a)^(2)* (w)^(2) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, z]+ (a)^(2)* (w)^(2) == 1</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [272 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .125000001+1.948557159*I
+| [https://dlmf.nist.gov/4.34.E10 4.34.E10] || <math qid="Q1870">\deriv{w}{z}+a^{2}w^{2} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{w}{z}+a^{2}w^{2} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, z)+ (a)^(2)* (w)^(2) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, z]+ (a)^(2)* (w)^(2) == 1</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [272 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .125000001+1.948557159*I
 Test Values: {a = -1.5, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .125000001+1.948557159*I
 Test Values: {a = -1.5, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .125000001+1.948557159*I
@@ Line 58: / Line 58: @@
 Test Values: {Rule[a, -1.5], 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/4.34.E11 4.34.E11] || [[Item:Q1871|<math>w = A\cosh@{az}+B\sinh@{az}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = A\cosh@{az}+B\sinh@{az}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w = A*cosh(a*z)+ B*sinh(a*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == A*Cosh[a*z]+ B*Sinh[a*z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6001928989+.561234643*I
+| [https://dlmf.nist.gov/4.34.E11 4.34.E11] || <math qid="Q1871">w = A\cosh@{az}+B\sinh@{az}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = A\cosh@{az}+B\sinh@{az}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w = A*cosh(a*z)+ B*sinh(a*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == A*Cosh[a*z]+ B*Sinh[a*z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6001928989+.561234643*I
 Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, a = -1.5, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.6457530113+1.981963256*I
 Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, a = -1.5, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .9837329493+.425340516e-1*I
@@ Line 66: / Line 66: @@
 Test Values: {Rule[a, -1.5], Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 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/4.34.E12 4.34.E12] || [[Item:Q1872|<math>w = (1/a)\sinh@{az+c}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = (1/a)\sinh@{az+c}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w = (1/a)*sinh(a*z + c)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == (1/a)*Sinh[a*z + c]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.126061208-3.246674013*I
+| [https://dlmf.nist.gov/4.34.E12 4.34.E12] || <math qid="Q1872">w = (1/a)\sinh@{az+c}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = (1/a)\sinh@{az+c}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w = (1/a)*sinh(a*z + c)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == (1/a)*Sinh[a*z + c]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.126061208-3.246674013*I
 Test Values: {a = -1.5, c = -1.5, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .7188715257-.3314459800*I
 Test Values: {a = -1.5, c = -1.5, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .265391293e-1+3.580357057*I
@@ Line 74: / Line 74: @@
 Test Values: {Rule[a, -1.5], Rule[c, -1.5], 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/4.34.E13 4.34.E13] || [[Item:Q1873|<math>w = (1/a)\cosh@{az+c}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = (1/a)\cosh@{az+c}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w = (1/a)*cosh(a*z + c)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == (1/a)*Cosh[a*z + c]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 4.887803259+4.219013756*I
+| [https://dlmf.nist.gov/4.34.E13 4.34.E13] || <math qid="Q1873">w = (1/a)\cosh@{az+c}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = (1/a)\cosh@{az+c}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w = (1/a)*cosh(a*z + c)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == (1/a)*Cosh[a*z + c]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 4.887803259+4.219013756*I
 Test Values: {a = -1.5, c = -1.5, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.097709449+1.028092043*I
 Test Values: {a = -1.5, c = -1.5, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.724372908-2.512669644*I
@@ Line 82: / Line 82: @@
 Test Values: {Rule[a, -1.5], Rule[c, -1.5], 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/4.34.E14 4.34.E14] || [[Item:Q1874|<math>w = (1/a)\coth@{az+c}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = (1/a)\coth@{az+c}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w = (1/a)*coth(a*z + c)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == (1/a)*Coth[a*z + c]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1990274306+.5049301211*I
+| [https://dlmf.nist.gov/4.34.E14 4.34.E14] || <math qid="Q1874">w = (1/a)\coth@{az+c}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = (1/a)\coth@{az+c}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w = (1/a)*coth(a*z + c)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == (1/a)*Coth[a*z + c]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1990274306+.5049301211*I
 Test Values: {a = -1.5, c = -1.5, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4235738270+.6074604561*I
 Test Values: {a = -1.5, c = -1.5, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2119596261+.4924838498*I

4.34: Difference between revisions

Latest revision as of 11:09, 28 June 2021

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