|
|
| (3 intermediate revisions by the same user not shown) |
| Line 1: |
Line 1: |
| {| class="wikitable sortable"
| | <div style="-moz-column-count:2; column-count:2;"> |
| |- | | ; Notation : [[11.1|11.1 Special Notation]]<br> |
| ! DLMF !! Formula !! Constraints !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica
| | ; Struve and Modified Struve Functions : [[11.2|11.2 Definitions]]<br>[[11.3|11.3 Graphics]]<br>[[11.4|11.4 Basic Properties]]<br>[[11.5|11.5 Integral Representations]]<br>[[11.6|11.6 Asymptotic Expansions]]<br>[[11.7|11.7 Integrals and Sums]]<br>[[11.8|11.8 Analogs to Kelvin Functions]]<br> |
| |-
| | ; Related Functions : [[11.9|11.9 Lommel Functions]]<br>[[11.10|11.10 Anger–Weber Functions]]<br>[[11.11|11.11 Asymptotic Expansions of Anger–Weber Functions]]<br> |
| | [https://dlmf.nist.gov/11.2.E1 11.2.E1] || [[Item:Q3916|<math>\StruveH{\nu}@{z} = (\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(-1)^{n}(\tfrac{1}{2}z)^{2n}}{\EulerGamma@{n+\tfrac{3}{2}}\EulerGamma@{n+\nu+\tfrac{3}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{\nu}@{z} = (\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(-1)^{n}(\tfrac{1}{2}z)^{2n}}{\EulerGamma@{n+\tfrac{3}{2}}\EulerGamma@{n+\nu+\tfrac{3}{2}}}</syntaxhighlight> || <math>\realpart@@{n+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(nu, z) = ((1)/(2)*z)^(nu + 1)* sum(((- 1)^(n)*((1)/(2)*z)^(2*n))/(GAMMA(n +(3)/(2))*GAMMA(n + nu +(3)/(2))), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[\[Nu], z] == (Divide[1,2]*z)^(\[Nu]+ 1)* Sum[Divide[(- 1)^(n)*(Divide[1,2]*z)^(2*n),Gamma[n +Divide[3,2]]*Gamma[n + \[Nu]+Divide[3,2]]], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
| | ; Applications : [[11.12|11.12 Physical Applications]]<br> |
| |-
| | ; Computation : [[11.13|11.13 Methods of Computation]]<br>[[11.14|11.14 Tables]]<br>[[11.15|11.15 Approximations]]<br>[[11.16|11.16 Software]]<br> |
| | [https://dlmf.nist.gov/11.2.E2 11.2.E2] || [[Item:Q3917|<math>\modStruveL{\nu}@{z} = -ie^{-\frac{1}{2}\pi i\nu}\StruveH{\nu}@{iz}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveL{\nu}@{z} = -ie^{-\frac{1}{2}\pi i\nu}\StruveH{\nu}@{iz}</syntaxhighlight> || <math>\realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveL(nu, z) = - I*exp(-(1)/(2)*Pi*I*nu)*StruveH(nu, I*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[\[Nu], z] == - I*Exp[-Divide[1,2]*Pi*I*\[Nu]]*StruveH[\[Nu], I*z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [8 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.240284959+1.629557917*I
| | </div> |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 33.65868914+29.08337177*I
| |
| Test Values: {nu = -1/2+1/2*I*3^(1/2), z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [8 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.2402849561066787, 1.6295579188731661]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[33.658689094091635, 29.08337174056143]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.2.E2 11.2.E2] || [[Item:Q3917|<math>-ie^{-\frac{1}{2}\pi i\nu}\StruveH{\nu}@{iz} = (\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(\tfrac{1}{2}z)^{2n}}{\EulerGamma@{n+\tfrac{3}{2}}\EulerGamma@{n+\nu+\tfrac{3}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-ie^{-\frac{1}{2}\pi i\nu}\StruveH{\nu}@{iz} = (\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(\tfrac{1}{2}z)^{2n}}{\EulerGamma@{n+\tfrac{3}{2}}\EulerGamma@{n+\nu+\tfrac{3}{2}}}</syntaxhighlight> || <math>\realpart@@{n+\nu+\tfrac{3}{2}} > 0, \realpart@@{n+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>- I*exp(-(1)/(2)*Pi*I*nu)*StruveH(nu, I*z) = ((1)/(2)*z)^(nu + 1)* sum((((1)/(2)*z)^(2*n))/(GAMMA(n +(3)/(2))*GAMMA(n + nu +(3)/(2))), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>- I*Exp[-Divide[1,2]*Pi*I*\[Nu]]*StruveH[\[Nu], I*z] == (Divide[1,2]*z)^(\[Nu]+ 1)* Sum[Divide[(Divide[1,2]*z)^(2*n),Gamma[n +Divide[3,2]]*Gamma[n + \[Nu]+Divide[3,2]]], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [8 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.240284959-1.629557917*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -33.65868914-29.08337177*I
| |
| Test Values: {nu = -1/2+1/2*I*3^(1/2), z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [8 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.2402849561066787, -1.6295579188731661]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-33.658689094091635, -29.08337174056143]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.2.E5 11.2.E5] || [[Item:Q3920|<math>\StruveK{\nu}@{z} = \StruveH{\nu}@{z}-\BesselY{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveK{\nu}@{z} = \StruveH{\nu}@{z}-\BesselY{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{\nu+k+1} > 0, \realpart@@{-\nu+k+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(nu, z) - BesselY(nu, z) = StruveH(nu, z)- BesselY(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[\[Nu], z] - BesselY[\[Nu], z] == StruveH[\[Nu], z]- BesselY[\[Nu], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.2.E6 11.2.E6] || [[Item:Q3921|<math>\modStruveM{\nu}@{z} = \modStruveL{\nu}@{z}-\modBesselI{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveM{\nu}@{z} = \modStruveL{\nu}@{z}-\modBesselI{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{\nu+k+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveL(nu, z) - BesselI(nu, z) = StruveL(nu, z)- BesselI(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[\[Nu], z] - BesselI[\[Nu], z] == StruveL[\[Nu], z]- BesselI[\[Nu], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.2.E7 11.2.E7] || [[Item:Q3922|<math>\deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}+\left(1-\frac{\nu^{2}}{z^{2}}\right)w = \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}+\left(1-\frac{\nu^{2}}{z^{2}}\right)w = \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}</syntaxhighlight> || <math>\realpart@@{\nu+\tfrac{1}{2}} > 0</math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)])+(1)/(z)*diff(w, z)+(1 -((nu)^(2))/((z)^(2)))*w = (((1)/(2)*z)^(nu - 1))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}]+Divide[1,z]*D[w, z]+(1 -Divide[\[Nu]^(2),(z)^(2)])*w == Divide[(Divide[1,2]*z)^(\[Nu]- 1),Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.5630887369+.2307852889*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.502962248+1.156533180*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.563088736999922, 0.23078528896155245]
| |
| Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.3603758852198513, 0.9342077190875079]
| |
| Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.2.E8 11.2.E8] || [[Item:Q3923|<math>w = \StruveH{\nu}@{z},\StruveK{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveH{\nu}@{z},\StruveK{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{n+\nu+\tfrac{3}{2}} > 0, \realpart@@{\nu+k+1} > 0, \realpart@@{-\nu+k+1} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, z); StruveH(nu, z) - BesselY(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], z]
| |
| StruveH[\[Nu], z] - BesselY[\[Nu], z]</syntaxhighlight> || Failure || Failure || Error || Error
| |
| |-
| |
| | [https://dlmf.nist.gov/11.2.E9 11.2.E9] || [[Item:Q3924|<math>\deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}-\left(1+\frac{\nu^{2}}{z^{2}}\right)w = \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}-\left(1+\frac{\nu^{2}}{z^{2}}\right)w = \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}</syntaxhighlight> || <math>\realpart@@{\nu+\tfrac{1}{2}} > 0</math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)])+(1)/(z)*diff(w, z)-(1 +((nu)^(2))/((z)^(2)))*w = (((1)/(2)*z)^(nu - 1))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}]+Divide[1,z]*D[w, z]-(1 +Divide[\[Nu]^(2),(z)^(2)])*w == Divide[(Divide[1,2]*z)^(\[Nu]- 1),Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.295139545-.7692147111*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2290885595+.1565331804*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.2951395445687996, -0.7692147110384474]
| |
| Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.0924266927887287, -0.06579228091249201]
| |
| Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.2.E10 11.2.E10] || [[Item:Q3925|<math>w = \modStruveL{\nu}@{z},\modStruveM{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \modStruveL{\nu}@{z},\modStruveM{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{\nu+k+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveL(nu, z); StruveL(nu, z) - BesselI(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveL[\[Nu], z]
| |
| StruveL[\[Nu], z] - BesselI[\[Nu], z]</syntaxhighlight> || Failure || Failure || Error || Error
| |
| |-
| |
| | [https://dlmf.nist.gov/11.2.E11 11.2.E11] || [[Item:Q3926|<math>w = \StruveH{\nu}@{x}+A\BesselJ{\nu}@{x}+B\BesselY{\nu}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveH{\nu}@{x}+A\BesselJ{\nu}@{x}+B\BesselY{\nu}@{x}</syntaxhighlight> || <math>\realpart@@{\nu+k+1} > 0, \realpart@@{-\nu+k+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, x)+ A*BesselJ(nu, x)+ B*BesselY(nu, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], x]+ A*BesselJ[\[Nu], x]+ B*BesselY[\[Nu], x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.568729179e-1+1.004857129*I
| |
| Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.306236381+1.613216681*I
| |
| Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.056872918319905263, 1.0048571288175818]
| |
| Test Values: {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[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.7531990546092198, -1.6096988531229037]
| |
| Test Values: {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[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.2.E12 11.2.E12] || [[Item:Q3927|<math>w = \StruveK{\nu}@{x}+A\BesselJ{\nu}@{x}+B\BesselY{\nu}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveK{\nu}@{x}+A\BesselJ{\nu}@{x}+B\BesselY{\nu}@{x}</syntaxhighlight> || <math>\realpart@@{\nu+k+1} > 0, \realpart@@{-\nu+k+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, x) - BesselY(nu, x)+ A*BesselJ(nu, x)+ B*BesselY(nu, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], x] - BesselY[\[Nu], x]+ A*BesselJ[\[Nu], x]+ B*BesselY[\[Nu], x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4449553305+.6668360043*I
| |
| Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1477245032+1.196204678*I
| |
| Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.4449553308212987, 0.6668360040225405]
| |
| Test Values: {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[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.2518593906559602, -2.1242453536287655]
| |
| Test Values: {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[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.2.E13 11.2.E13] || [[Item:Q3928|<math>w = \StruveH{\nu}@{z}+A\BesselJ{\nu}@{z}+B\HankelH{1}{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveH{\nu}@{z}+A\BesselJ{\nu}@{z}+B\HankelH{1}{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{\nu+k+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, z)+ A*BesselJ(nu, z)+ B*HankelH1(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], z]+ A*BesselJ[\[Nu], z]+ B*HankelH1[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4180841979+.8728935730*I
| |
| Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.928541044+.4861253769*I
| |
| Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.4180841980733331, 0.8728935728522607]
| |
| Test Values: {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]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.285405641595042, -1.3320778184897675]
| |
| Test Values: {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]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.2.E14 11.2.E14] || [[Item:Q3929|<math>w = \StruveH{\nu}@{z}+A\BesselJ{\nu}@{z}+B\HankelH{2}{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveH{\nu}@{z}+A\BesselJ{\nu}@{z}+B\HankelH{2}{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{\nu+k+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, z)+ A*BesselJ(nu, z)+ B*HankelH2(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], z]+ A*BesselJ[\[Nu], z]+ B*HankelH2[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1098269700-.5965662020*I
| |
| Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .3171413600-.3710144720*I
| |
| Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.109826969919957, -0.5965662019254474]
| |
| Test Values: {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]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.9889109079558663, -0.015623729667162342]
| |
| Test Values: {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]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.2.E15 11.2.E15] || [[Item:Q3930|<math>w = \StruveK{\nu}@{z}+A\HankelH{1}{\nu}@{z}+B\HankelH{2}{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveK{\nu}@{z}+A\HankelH{1}{\nu}@{z}+B\HankelH{2}{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{\nu+k+1} > 0, \realpart@@{-\nu+k+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, z) - BesselY(nu, z)+ A*HankelH1(nu, z)+ B*HankelH2(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], z] - BesselY[\[Nu], z]+ A*HankelH1[\[Nu], z]+ B*HankelH2[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.9224011534+.2769363875*I
| |
| Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.154538681+.9695969456*I
| |
| Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.9224011534734378, 0.27693638794598185]
| |
| Test Values: {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]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.3912406162671118, -1.5643629838862487]
| |
| Test Values: {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]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.2.E16 11.2.E16] || [[Item:Q3931|<math>w = \modStruveL{\nu}@{z}+A\modBesselK{\nu}@{z}+B\modBesselI{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \modStruveL{\nu}@{z}+A\modBesselK{\nu}@{z}+B\modBesselI{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{\nu+k+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveL(nu, z)+ A*BesselK(nu, z)+ B*BesselI(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveL[\[Nu], z]+ A*BesselK[\[Nu], z]+ B*BesselI[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4427134717+.1412701443*I
| |
| Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8499113341+3.412421345*I
| |
| Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.4427134718200613, 0.1412701442672558]
| |
| Test Values: {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]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.8647663358395983, -0.37009195882490975]
| |
| Test Values: {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]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.2.E17 11.2.E17] || [[Item:Q3932|<math>w = \modStruveM{\nu}@{z}+A\modBesselK{\nu}@{z}+B\modBesselI{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \modStruveM{\nu}@{z}+A\modBesselK{\nu}@{z}+B\modBesselI{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{\nu+k+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveL(nu, z) - BesselI(nu, z)+ A*BesselK(nu, z)+ B*BesselI(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveL[\[Nu], z] - BesselI[\[Nu], z]+ A*BesselK[\[Nu], z]+ B*BesselI[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .876284277e-1+.1517241441*I
| |
| Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .9234962821+3.599925727*I
| |
| Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.08762842754807953, 0.15172414402816306]
| |
| Test Values: {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]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.09828151494898707, -0.22324970290386212]
| |
| Test Values: {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]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E1 11.4.E1] || [[Item:Q3933|<math>\StruveK{n+\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sum_{m=0}^{n}\frac{(2m)!\,2^{-2m}}{m!\,(n-m)!}\,(\tfrac{1}{2}z)^{n-2m}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveK{n+\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sum_{m=0}^{n}\frac{(2m)!\,2^{-2m}}{m!\,(n-m)!}\,(\tfrac{1}{2}z)^{n-2m}</syntaxhighlight> || <math>\realpart@@{n+\frac{1}{2}+k+1} > 0, \realpart@@{-n+\frac{1}{2}+k+1} > 0, \realpart@@{n+n+\frac{1}{2}+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(n +(1)/(2), z) - BesselY(n +(1)/(2), z) = ((2)/(Pi*z))^((1)/(2))* sum((factorial(2*m)*(2)^(- 2*m))/(factorial(m)*factorial(n - m))*((1)/(2)*z)^(n - 2*m), m = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[n +Divide[1,2], z] - BesselY[n +Divide[1,2], z] == (Divide[2,Pi*z])^(Divide[1,2])* Sum[Divide[(2*m)!*(2)^(- 2*m),(m)!*(n - m)!]*(Divide[1,2]*z)^(n - 2*m), {m, 0, n}, GenerateConditions->None]</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[0.9229158558166265, Times[-0.4886025119029198, DifferenceRoot[Function[{, }
| |
| Test Values: {Equal[Plus[Times[4, []], Times[Plus[-18, Times[-8, ]], [Plus[1, ]]], Times[Plus[30, Times[22, ], Times[4, Power[, 2]], Power[1.5, 2]], [Plus[2, ]]], Times[-1, Plus[3, ], Power[1.5, 2], [Plus[3, ]]]], 0], Equal[[1], Plus[1, Times[2, Power[1.5, -2]]]], Equal[[2], Plus[Rational[1, 2], Times[12, Power[1.5, -4]], Times[2, Power[1.5, -2]]]], Equal[[3], Plus[Rational[1, 6], Times[120, Power[1.5, -6]], Times[12, Power[1.5, -4]], Power[1.5, -2]]], Equal[[4], Plus[Rational[1, 24], Times[1680, Power[1.5, -8]], Times[120, Power[1.5, -6]], Times[6, Power[1.5, -4]], Times[Rational[1, 3], Power[1.5, -2]]]]}]][1.0]]], {Rule[n, 1], Rule[z, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[1.3775876377262881, Times[-0.36645188392718997, DifferenceRoot[Function[{, }
| |
| Test Values: {Equal[Plus[Times[4, []], Times[Plus[-18, Time</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E2 11.4.E2] || [[Item:Q3934|<math>\modStruveL{n+\frac{1}{2}}@{z} = \modBesselI{-n-\frac{1}{2}}@{z}-\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sum_{m=0}^{n}\frac{(-1)^{m}(2m)!\,2^{-2m}}{m!\,(n-m)!}\,(\tfrac{1}{2}z)^{n-2m}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveL{n+\frac{1}{2}}@{z} = \modBesselI{-n-\frac{1}{2}}@{z}-\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sum_{m=0}^{n}\frac{(-1)^{m}(2m)!\,2^{-2m}}{m!\,(n-m)!}\,(\tfrac{1}{2}z)^{n-2m}</syntaxhighlight> || <math>\realpart@@{-n-\frac{1}{2}+k+1} > 0, \realpart@@{n+n+\frac{1}{2}+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveL(n +(1)/(2), z) = BesselI(- n -(1)/(2), z)-((2)/(Pi*z))^((1)/(2))* sum(((- 1)^(m)*factorial(2*m)*(2)^(- 2*m))/(factorial(m)*factorial(n - m))*((1)/(2)*z)^(n - 2*m), m = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[n +Divide[1,2], z] == BesselI[- n -Divide[1,2], z]-(Divide[2,Pi*z])^(Divide[1,2])* Sum[Divide[(- 1)^(m)*(2*m)!*(2)^(- 2*m),(m)!*(n - m)!]*(Divide[1,2]*z)^(n - 2*m), {m, 0, n}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 21] || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[-0.05428916798921324, Times[0.4886025119029198, DifferenceRoot[Function[{, }
| |
| Test Values: {Equal[Plus[Times[4, []], Times[Plus[-18, Times[-8, ]], [Plus[1, ]]], Times[Plus[30, Times[22, ], Times[4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[3, ], Power[1.5, 2], [Plus[3, ]]]], 0], Equal[[1], Plus[1, Times[-2, Power[1.5, -2]]]], Equal[[2], Plus[Rational[1, 2], Times[12, Power[1.5, -4]], Times[-2, Power[1.5, -2]]]], Equal[[3], Plus[Rational[1, 6], Times[-120, Power[1.5, -6]], Times[12, Power[1.5, -4]], Times[-1, Power[1.5, -2]]]], Equal[[4], Plus[Rational[1, 24], Times[1680, Power[1.5, -8]], Times[-120, Power[1.5, -6]], Times[6, Power[1.5, -4]], Times[Rational[-1, 3], Power[1.5, -2]]]]}]][1.0]]], {Rule[n, 1], Rule[z, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[-0.726117621855728, Times[0.36645188392718997, DifferenceRoot[Function[{, }
| |
| Test Values: {Equal[Plus[Times[4, []</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E3 11.4.E3] || [[Item:Q3935|<math>\StruveH{-n-\frac{1}{2}}@{z} = (-1)^{n}\BesselJ{n+\frac{1}{2}}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{-n-\frac{1}{2}}@{z} = (-1)^{n}\BesselJ{n+\frac{1}{2}}@{z}</syntaxhighlight> || <math>\realpart@@{n+\frac{1}{2}+k+1} > 0, \realpart@@{n+-n-\frac{1}{2}+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(- n -(1)/(2), z) = (- 1)^(n)* BesselJ(n +(1)/(2), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[- n -Divide[1,2], z] == (- 1)^(n)* BesselJ[n +Divide[1,2], z]</syntaxhighlight> || Failure || Failure || Successful [Tested: 21] || Successful [Tested: 21]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E4 11.4.E4] || [[Item:Q3936|<math>\modStruveL{-n-\frac{1}{2}}@{z} = \modBesselI{n+\frac{1}{2}}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveL{-n-\frac{1}{2}}@{z} = \modBesselI{n+\frac{1}{2}}@{z}</syntaxhighlight> || <math>\realpart@@{n+\frac{1}{2}+k+1} > 0, \realpart@@{n+-n-\frac{1}{2}+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveL(- n -(1)/(2), z) = BesselI(n +(1)/(2), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[- n -Divide[1,2], z] == BesselI[n +Divide[1,2], z]</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 21]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E5 11.4.E5] || [[Item:Q3937|<math>\StruveH{\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}(1-\cos@@{z})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}(1-\cos@@{z})</syntaxhighlight> || <math>\realpart@@{n+\frac{1}{2}+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH((1)/(2), z) = ((2)/(Pi*z))^((1)/(2))*(1 - cos(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[Divide[1,2], z] == (Divide[2,Pi*z])^(Divide[1,2])*(1 - Cos[z])</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E6 11.4.E6] || [[Item:Q3938|<math>\StruveH{-\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sin@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{-\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sin@@{z}</syntaxhighlight> || <math>\realpart@@{n+-\frac{1}{2}+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(-(1)/(2), z) = ((2)/(Pi*z))^((1)/(2))* sin(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[-Divide[1,2], z] == (Divide[2,Pi*z])^(Divide[1,2])* Sin[z]</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E7 11.4.E7] || [[Item:Q3939|<math>\modStruveL{\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}(\cosh@@{z}-1)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveL{\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}(\cosh@@{z}-1)</syntaxhighlight> || <math>\realpart@@{n+\frac{1}{2}+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveL((1)/(2), z) = ((2)/(Pi*z))^((1)/(2))*(cosh(z)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[Divide[1,2], z] == (Divide[2,Pi*z])^(Divide[1,2])*(Cosh[z]- 1)</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E8 11.4.E8] || [[Item:Q3940|<math>\modStruveL{-\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sinh@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveL{-\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sinh@@{z}</syntaxhighlight> || <math>\realpart@@{n+-\frac{1}{2}+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveL(-(1)/(2), z) = ((2)/(Pi*z))^((1)/(2))* sinh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[-Divide[1,2], z] == (Divide[2,Pi*z])^(Divide[1,2])* Sinh[z]</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E9 11.4.E9] || [[Item:Q3941|<math>\StruveH{\frac{3}{2}}@{z} = \left(\frac{z}{2\pi}\right)^{\frac{1}{2}}\left(1+\frac{2}{z^{2}}\right)-\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\left(\sin@@{z}+\frac{\cos@@{z}}{z}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{\frac{3}{2}}@{z} = \left(\frac{z}{2\pi}\right)^{\frac{1}{2}}\left(1+\frac{2}{z^{2}}\right)-\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\left(\sin@@{z}+\frac{\cos@@{z}}{z}\right)</syntaxhighlight> || <math>\realpart@@{n+\frac{3}{2}+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH((3)/(2), z) = ((z)/(2*Pi))^((1)/(2))*(1 +(2)/((z)^(2)))-((2)/(Pi*z))^((1)/(2))*(sin(z)+(cos(z))/(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[Divide[3,2], z] == (Divide[z,2*Pi])^(Divide[1,2])*(1 +Divide[2,(z)^(2)])-(Divide[2,Pi*z])^(Divide[1,2])*(Sin[z]+Divide[Cos[z],z])</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E10 11.4.E10] || [[Item:Q3942|<math>\StruveH{-\frac{3}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\left(\cos@@{z}-\frac{\sin@@{z}}{z}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{-\frac{3}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\left(\cos@@{z}-\frac{\sin@@{z}}{z}\right)</syntaxhighlight> || <math>\realpart@@{n+-\frac{3}{2}+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(-(3)/(2), z) = ((2)/(Pi*z))^((1)/(2))*(cos(z)-(sin(z))/(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[-Divide[3,2], z] == (Divide[2,Pi*z])^(Divide[1,2])*(Cos[z]-Divide[Sin[z],z])</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E11 11.4.E11] || [[Item:Q3943|<math>\modStruveL{\frac{3}{2}}@{z} = -\left(\frac{z}{2\pi}\right)^{\frac{1}{2}}\left(1-\frac{2}{z^{2}}\right)+\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\left(\sinh@@{z}-\frac{\cosh@@{z}}{z}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveL{\frac{3}{2}}@{z} = -\left(\frac{z}{2\pi}\right)^{\frac{1}{2}}\left(1-\frac{2}{z^{2}}\right)+\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\left(\sinh@@{z}-\frac{\cosh@@{z}}{z}\right)</syntaxhighlight> || <math>\realpart@@{n+\frac{3}{2}+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveL((3)/(2), z) = -((z)/(2*Pi))^((1)/(2))*(1 -(2)/((z)^(2)))+((2)/(Pi*z))^((1)/(2))*(sinh(z)-(cosh(z))/(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[Divide[3,2], z] == -(Divide[z,2*Pi])^(Divide[1,2])*(1 -Divide[2,(z)^(2)])+(Divide[2,Pi*z])^(Divide[1,2])*(Sinh[z]-Divide[Cosh[z],z])</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E12 11.4.E12] || [[Item:Q3944|<math>\modStruveL{-\frac{3}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\left(\cosh@@{z}-\frac{\sinh@@{z}}{z}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveL{-\frac{3}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\left(\cosh@@{z}-\frac{\sinh@@{z}}{z}\right)</syntaxhighlight> || <math>\realpart@@{n+-\frac{3}{2}+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveL(-(3)/(2), z) = ((2)/(Pi*z))^((1)/(2))*(cosh(z)-(sinh(z))/(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[-Divide[3,2], z] == (Divide[2,Pi*z])^(Divide[1,2])*(Cosh[z]-Divide[Sinh[z],z])</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E13 11.4.E13] || [[Item:Q3945|<math>\StruveH{\nu}@{x} \geq 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{\nu}@{x} \geq 0</syntaxhighlight> || <math>x > 0, \nu \geq \tfrac{1}{2}, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(nu, x) >= 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[\[Nu], x] >= 0</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E14 11.4.E14] || [[Item:Q3946|<math>\StruveH{\nu}@{z} = \frac{2(\tfrac{1}{2}z)^{\nu+1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}(1+\vartheta)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{\nu}@{z} = \frac{2(\tfrac{1}{2}z)^{\nu+1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}(1+\vartheta)</syntaxhighlight> || <math>\nu \neq -\tfrac{3}{2}, \realpart@@{\nu+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(nu, z) = (2*((1)/(2)*z)^(nu + 1))/(sqrt(Pi)*GAMMA(nu +(3)/(2)))*(1 + vartheta)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[\[Nu], z] == Divide[2*(Divide[1,2]*z)^(\[Nu]+ 1),Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]]*(1 + \[CurlyTheta])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1471445522-.1672488986*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, vartheta = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1483631977-.1537807385*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, vartheta = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.14714455195987888, -0.16724889870966364]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϑ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.8437410873580948, -0.4272690725617171]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϑ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E15 11.4.E15] || [[Item:Q3947|<math>|\vartheta| < \frac{2}{3}\exp@{\frac{\tfrac{1}{4}|z|^{2}}{|\nu_{0}+\tfrac{3}{2}|}-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>|\vartheta| < \frac{2}{3}\exp@{\frac{\tfrac{1}{4}|z|^{2}}{|\nu_{0}+\tfrac{3}{2}|}-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>abs(vartheta) < (2)/(3)*exp(((1)/(4)*(abs(z))^(2))/(abs(nu[0]+(3)/(2)))- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[\[CurlyTheta]] < Divide[2,3]*Exp[Divide[Divide[1,4]*(Abs[z])^(2),Abs[Subscript[\[Nu], 0]+Divide[3,2]]]- 1]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1. < .2719639306
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, vartheta = 1/2*3^(1/2)+1/2*I, nu[0] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1. < .2962703575
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, vartheta = 1/2*3^(1/2)+1/2*I, nu[0] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: False
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϑ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ν, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: False
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϑ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ν, 0], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E16 11.4.E16] || [[Item:Q3948|<math>\StruveH{\nu}@{ze^{m\pi i}} = e^{m\pi i(\nu+1)}\StruveH{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{\nu}@{ze^{m\pi i}} = e^{m\pi i(\nu+1)}\StruveH{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(nu, z*exp(m*Pi*I)) = exp(m*Pi*I*(nu + 1))*StruveH(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[\[Nu], z*Exp[m*Pi*I]] == Exp[m*Pi*I*(\[Nu]+ 1)]*StruveH[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [36 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7482205956+.6031447740*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.4043537260-.2594960110*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2), m = 3}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [48 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.7482205967366697, 0.6031447730973842]
| |
| Test Values: {Rule[m, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.8264714651575658, -11.333535783044978]
| |
| Test Values: {Rule[m, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E17 11.4.E17] || [[Item:Q3949|<math>\modStruveL{\nu}@{ze^{m\pi i}} = e^{m\pi i(\nu+1)}\modStruveL{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveL{\nu}@{ze^{m\pi i}} = e^{m\pi i(\nu+1)}\modStruveL{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveL(nu, z*exp(m*Pi*I)) = exp(m*Pi*I*(nu + 1))*StruveL(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[\[Nu], z*Exp[m*Pi*I]] == Exp[m*Pi*I*(\[Nu]+ 1)]*StruveL[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [36 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7484016339+.7418531852*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.3910618545-.1976660760*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2), m = 3}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [48 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.7484016356562583, 0.741853184386289]
| |
| Test Values: {Rule[m, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.1393494415684403, -14.42209495054837]
| |
| Test Values: {Rule[m, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E18 11.4.E18] || [[Item:Q3950|<math>\StruveH{\nu}@{z} = \frac{4}{\pi^{1/2}\EulerGamma@{\nu+\tfrac{1}{2}}}\*\sum_{k=0}^{\infty}\frac{(2k+\nu+1)\EulerGamma@{k+\nu+1}}{k!(2k+1)(2k+2\nu+1)}\BesselJ{2k+\nu+1}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{\nu}@{z} = \frac{4}{\pi^{1/2}\EulerGamma@{\nu+\tfrac{1}{2}}}\*\sum_{k=0}^{\infty}\frac{(2k+\nu+1)\EulerGamma@{k+\nu+1}}{k!(2k+1)(2k+2\nu+1)}\BesselJ{2k+\nu+1}@{z}</syntaxhighlight> || <math>\realpart@@{2k+\nu+1+k+1} > 0, \realpart@@{\nu+\tfrac{1}{2}} > 0, \realpart@@{k+\nu+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(nu, z) = (4)/((Pi)^(1/2)* GAMMA(nu +(1)/(2)))* sum(((2*k + nu + 1)*GAMMA(k + nu + 1))/(factorial(k)*(2*k + 1)*(2*k + 2*nu + 1))*BesselJ(2*k + nu + 1, z), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[\[Nu], z] == Divide[4,(Pi)^(1/2)* Gamma[\[Nu]+Divide[1,2]]]* Sum[Divide[(2*k + \[Nu]+ 1)*Gamma[k + \[Nu]+ 1],(k)!*(2*k + 1)*(2*k + 2*\[Nu]+ 1)]*BesselJ[2*k + \[Nu]+ 1, z], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || <div class="toccolours mw-collapsible mw-collapsed">Failed [35 / 35]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.19324594490102928, 0.050519652606000824], Times[Complex[-2.8810800784728325, -0.07996643500485433], NSum[Times[Power[Plus[1, Times[2, k]], -1], Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Times[2, k]], Power[Plus[1, Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, k]], -1], BesselJ[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Times[2, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[Factorial[k], -1], Gamma[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k]]]
| |
| Test Values: {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.11400577441337441, 0.7764453237975459], Times[Complex[-3.5865453830779916, 1.1372180444285063], NSum[Times[Power[Plus[1, Times[2, k]], -1], P</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E19 11.4.E19] || [[Item:Q3951|<math>\StruveH{\nu}@{z} = \left(\frac{z}{2\pi}\right)^{1/2}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{2}z)^{k}}{k!(k+\tfrac{1}{2})}\BesselJ{k+\nu+\frac{1}{2}}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{\nu}@{z} = \left(\frac{z}{2\pi}\right)^{1/2}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{2}z)^{k}}{k!(k+\tfrac{1}{2})}\BesselJ{k+\nu+\frac{1}{2}}@{z}</syntaxhighlight> || <math>\realpart@@{k+\nu+\frac{1}{2}+k+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(nu, z) = ((z)/(2*Pi))^(1/2)* sum((((1)/(2)*z)^(k))/(factorial(k)*(k +(1)/(2)))*BesselJ(k + nu +(1)/(2), z), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[\[Nu], z] == (Divide[z,2*Pi])^(1/2)* Sum[Divide[(Divide[1,2]*z)^(k),(k)!*(k +Divide[1,2])]*BesselJ[k + \[Nu]+Divide[1,2], z], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.19324594490102928, 0.050519652606000824], Times[Complex[-0.38534865183839906, -0.10325386006452089], NSum[Times[Power[2, Times[-1, k]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], Power[Plus[Rational[1, 2], k], -1], BesselJ[Plus[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[Factorial[k], -1]]
| |
| Test Values: {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.7460861755377195, -0.054406581179451755], Times[Complex[-0.38534865183839906, -0.10325386006452089], NSum[Times[Power[2, Times[-1, k]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], Power[Plus[Rational[1, 2], k], -1], BesselJ[Plus[Rational[1, 2], Power[E, Times[Complex[</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E20 11.4.E20] || [[Item:Q3952|<math>\StruveH{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu+\frac{1}{2}}}{\EulerGamma@{\nu+\tfrac{1}{2}}}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{2}z)^{k}}{k!(k+\nu+\tfrac{1}{2})}\BesselJ{k+\frac{1}{2}}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu+\frac{1}{2}}}{\EulerGamma@{\nu+\tfrac{1}{2}}}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{2}z)^{k}}{k!(k+\nu+\tfrac{1}{2})}\BesselJ{k+\frac{1}{2}}@{z}</syntaxhighlight> || <math>\realpart@@{k+\frac{1}{2}+k+1} > 0, \realpart@@{\nu+\tfrac{1}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(nu, z) = (((1)/(2)*z)^(nu +(1)/(2)))/(GAMMA(nu +(1)/(2)))*sum((((1)/(2)*z)^(k))/(factorial(k)*(k + nu +(1)/(2)))*BesselJ(k +(1)/(2), z), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[\[Nu], z] == Divide[(Divide[1,2]*z)^(\[Nu]+Divide[1,2]),Gamma[\[Nu]+Divide[1,2]]]*Sum[Divide[(Divide[1,2]*z)^(k),(k)!*(k + \[Nu]+Divide[1,2])]*BesselJ[k +Divide[1,2], z], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 35] || <div class="toccolours mw-collapsible mw-collapsed">Failed [35 / 35]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.19324594490102928, 0.050519652606000824], Times[Complex[-0.35177626861232025, -0.14724813153619726], NSum[Times[Power[2, Times[-1, k]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], Power[Plus[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], -1], BesselJ[Plus[Rational[1, 2], k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[Factorial[k], -1]]
| |
| Test Values: {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.11400577441337441, 0.7764453237975459], Times[Complex[-0.8980289919269182, -0.9563358827585198], NSum[Times[Power[2, Times[-1, k]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], Power[Plus[Rational[1, 2], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]], k], -1], Besse</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E21 11.4.E21] || [[Item:Q3953|<math>\StruveH{0}@{z} = \frac{4}{\pi}\sum_{k=0}^{\infty}\frac{\BesselJ{2k+1}@{z}}{2k+1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{0}@{z} = \frac{4}{\pi}\sum_{k=0}^{\infty}\frac{\BesselJ{2k+1}@{z}}{2k+1}</syntaxhighlight> || <math>\realpart@@{2k+1+k+1} > 0, \realpart@@{n+0+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(0, z) = (4)/(Pi)*sum((BesselJ(2*k + 1, z))/(2*k + 1), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[0, z] == Divide[4,Pi]*Sum[Divide[BesselJ[2*k + 1, z],2*k + 1], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E21 11.4.E21] || [[Item:Q3953|<math>\frac{4}{\pi}\sum_{k=0}^{\infty}\frac{\BesselJ{2k+1}@{z}}{2k+1} = 2\sum_{k=0}^{\infty}(-1)^{k}\BesselJ{k+\frac{1}{2}}^{2}@{\tfrac{1}{2}z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{4}{\pi}\sum_{k=0}^{\infty}\frac{\BesselJ{2k+1}@{z}}{2k+1} = 2\sum_{k=0}^{\infty}(-1)^{k}\BesselJ{k+\frac{1}{2}}^{2}@{\tfrac{1}{2}z}</syntaxhighlight> || <math>\realpart@@{2k+1+k+1} > 0, \realpart@@{n+0+\tfrac{3}{2}} > 0, \realpart@@{k+\frac{1}{2}+k+1} > 0</math> || <syntaxhighlight lang=mathematica>(4)/(Pi)*sum((BesselJ(2*k + 1, z))/(2*k + 1), k = 0..infinity) = 2*sum((- 1)^(k)* (BesselJ(k +(1)/(2), (1)/(2)*z))^(2), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[4,Pi]*Sum[Divide[BesselJ[2*k + 1, z],2*k + 1], {k, 0, Infinity}, GenerateConditions->None] == 2*Sum[(- 1)^(k)* (BesselJ[k +Divide[1,2], Divide[1,2]*z])^(2), {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.5489285468594604, 0.24901722825393072], Times[-2.0, NSum[Times[Power[-1, k], Power[BesselJ[Plus[Rational[1, 2], k], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], 2]]
| |
| Test Values: {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.39043053959878776, 0.5488285427518664], Times[-2.0, NSum[Times[Power[-1, k], Power[BesselJ[Plus[Rational[1, 2], k], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]], 2]]
| |
| Test Values: {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E22 11.4.E22] || [[Item:Q3954|<math>\StruveH{1}@{z} = \frac{2}{\pi}(1-\BesselJ{0}@{z})+\frac{4}{\pi}\sum_{k=1}^{\infty}\frac{\BesselJ{2k}@{z}}{4k^{2}-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{1}@{z} = \frac{2}{\pi}(1-\BesselJ{0}@{z})+\frac{4}{\pi}\sum_{k=1}^{\infty}\frac{\BesselJ{2k}@{z}}{4k^{2}-1}</syntaxhighlight> || <math>\realpart@@{0+k+1} > 0, \realpart@@{2k+k+1} > 0, \realpart@@{n+1+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(1, z) = (2)/(Pi)*(1 - BesselJ(0, z))+(4)/(Pi)*sum((BesselJ(2*k, z))/(4*(k)^(2)- 1), k = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[1, z] == Divide[2,Pi]*(1 - BesselJ[0, z])+Divide[4,Pi]*Sum[Divide[BesselJ[2*k, z],4*(k)^(2)- 1], {k, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E22 11.4.E22] || [[Item:Q3954|<math>\frac{2}{\pi}(1-\BesselJ{0}@{z})+\frac{4}{\pi}\sum_{k=1}^{\infty}\frac{\BesselJ{2k}@{z}}{4k^{2}-1} = 4\sum_{k=0}^{\infty}\BesselJ{2k+\frac{1}{2}}@{\tfrac{1}{2}z}\BesselJ{2k+\frac{3}{2}}@{\tfrac{1}{2}z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2}{\pi}(1-\BesselJ{0}@{z})+\frac{4}{\pi}\sum_{k=1}^{\infty}\frac{\BesselJ{2k}@{z}}{4k^{2}-1} = 4\sum_{k=0}^{\infty}\BesselJ{2k+\frac{1}{2}}@{\tfrac{1}{2}z}\BesselJ{2k+\frac{3}{2}}@{\tfrac{1}{2}z}</syntaxhighlight> || <math>\realpart@@{0+k+1} > 0, \realpart@@{2k+k+1} > 0, \realpart@@{n+1+\tfrac{3}{2}} > 0, \realpart@@{2k+\frac{1}{2}+k+1} > 0, \realpart@@{2k+\frac{3}{2}+k+1} > 0</math> || <syntaxhighlight lang=mathematica>(2)/(Pi)*(1 - BesselJ(0, z))+(4)/(Pi)*sum((BesselJ(2*k, z))/(4*(k)^(2)- 1), k = 1..infinity) = 4*sum(BesselJ(2*k +(1)/(2), (1)/(2)*z)*BesselJ(2*k +(3)/(2), (1)/(2)*z), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[2,Pi]*(1 - BesselJ[0, z])+Divide[4,Pi]*Sum[Divide[BesselJ[2*k, z],4*(k)^(2)- 1], {k, 1, Infinity}, GenerateConditions->None] == 4*Sum[BesselJ[2*k +Divide[1,2], Divide[1,2]*z]*BesselJ[2*k +Divide[3,2], Divide[1,2]*z], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.11277588530299563, 0.1715300454702578], Times[-4.0, NSum[Times[BesselJ[Plus[Rational[1, 2], Times[2, k]], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], BesselJ[Plus[Rational[3, 2], Times[2, k]], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]]
| |
| Test Values: {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.09862236423565694, -0.19602243923212043], Times[-4.0, NSum[Times[BesselJ[Plus[Rational[1, 2], Times[2, k]], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]], BesselJ[Plus[Rational[3, 2], Times[2, k]], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]]
| |
| Test Values: {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}<</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E23 11.4.E23] || [[Item:Q3955|<math>\StruveH{\nu-1}@{z}+\StruveH{\nu+1}@{z} = \frac{2\nu}{z}\StruveH{\nu}@{z}+\frac{(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{\nu-1}@{z}+\StruveH{\nu+1}@{z} = \frac{2\nu}{z}\StruveH{\nu}@{z}+\frac{(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}</syntaxhighlight> || <math>\realpart@@{\nu+\tfrac{3}{2}} > 0, \realpart@@{n+\nu-1+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+1+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(nu - 1, z)+ StruveH(nu + 1, z) = (2*nu)/(z)*StruveH(nu, z)+(((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[\[Nu]- 1, z]+ StruveH[\[Nu]+ 1, z] == Divide[2*\[Nu],z]*StruveH[\[Nu], z]+Divide[(Divide[1,2]*z)^\[Nu],Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 56] || Successful [Tested: 56]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E24 11.4.E24] || [[Item:Q3956|<math>\StruveH{\nu-1}@{z}-\StruveH{\nu+1}@{z} = 2\StruveH{\nu}'@{z}-\frac{(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{\nu-1}@{z}-\StruveH{\nu+1}@{z} = 2\StruveH{\nu}'@{z}-\frac{(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}</syntaxhighlight> || <math>\realpart@@{\nu+\tfrac{3}{2}} > 0, \realpart@@{n+\nu-1+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+1+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(nu - 1, z)- StruveH(nu + 1, z) = 2*diff( StruveH(nu, z), z$(1) )-(((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[\[Nu]- 1, z]- StruveH[\[Nu]+ 1, z] == 2*D[StruveH[\[Nu], z], {z, 1}]-Divide[(Divide[1,2]*z)^\[Nu],Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 56] || Successful [Tested: 56]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E25 11.4.E25] || [[Item:Q3957|<math>\modStruveL{\nu-1}@{z}-\modStruveL{\nu+1}@{z} = \frac{2\nu}{z}\modStruveL{\nu}@{z}+\frac{(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveL{\nu-1}@{z}-\modStruveL{\nu+1}@{z} = \frac{2\nu}{z}\modStruveL{\nu}@{z}+\frac{(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}</syntaxhighlight> || <math>\realpart@@{\nu+\tfrac{3}{2}} > 0, \realpart@@{n+\nu-1+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+1+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveL(nu - 1, z)- StruveL(nu + 1, z) = (2*nu)/(z)*StruveL(nu, z)+(((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[\[Nu]- 1, z]- StruveL[\[Nu]+ 1, z] == Divide[2*\[Nu],z]*StruveL[\[Nu], z]+Divide[(Divide[1,2]*z)^\[Nu],Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 56] || Successful [Tested: 56]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E26 11.4.E26] || [[Item:Q3958|<math>\modStruveL{\nu-1}@{z}+\modStruveL{\nu+1}@{z} = 2\modStruveL{\nu}'@{z}-\frac{(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveL{\nu-1}@{z}+\modStruveL{\nu+1}@{z} = 2\modStruveL{\nu}'@{z}-\frac{(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}</syntaxhighlight> || <math>\realpart@@{\nu+\tfrac{3}{2}} > 0, \realpart@@{n+\nu-1+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+1+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveL(nu - 1, z)+ StruveL(nu + 1, z) = 2*diff( StruveL(nu, z), z$(1) )-(((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[\[Nu]- 1, z]+ StruveL[\[Nu]+ 1, z] == 2*D[StruveL[\[Nu], z], {z, 1}]-Divide[(Divide[1,2]*z)^\[Nu],Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 56] || Successful [Tested: 56]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E27 11.4.E27] || [[Item:Q3959|<math>\deriv{}{z}\left(z^{\nu}\StruveH{\nu}@{z}\right) = z^{\nu}\StruveH{\nu-1}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\left(z^{\nu}\StruveH{\nu}@{z}\right) = z^{\nu}\StruveH{\nu-1}@{z}</syntaxhighlight> || <math>\realpart@@{n+\nu+\tfrac{3}{2}} > 0, \realpart@@{n+\nu-1+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>diff((z)^(nu)* StruveH(nu, z), z) = (z)^(nu)* StruveH(nu - 1, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[(z)^\[Nu]* StruveH[\[Nu], z], z] == (z)^\[Nu]* StruveH[\[Nu]- 1, z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 70] || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E28 11.4.E28] || [[Item:Q3960|<math>\deriv{}{z}\left(z^{-\nu}\StruveH{\nu}@{z}\right) = \frac{2^{-\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}-z^{-\nu}\StruveH{\nu+1}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\left(z^{-\nu}\StruveH{\nu}@{z}\right) = \frac{2^{-\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}-z^{-\nu}\StruveH{\nu+1}@{z}</syntaxhighlight> || <math>\realpart@@{\nu+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+1+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>diff((z)^(- nu)* StruveH(nu, z), z) = ((2)^(- nu))/(sqrt(Pi)*GAMMA(nu +(3)/(2)))- (z)^(- nu)* StruveH(nu + 1, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[(z)^(- \[Nu])* StruveH[\[Nu], z], z] == Divide[(2)^(- \[Nu]),Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]]- (z)^(- \[Nu])* StruveH[\[Nu]+ 1, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 56]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E29 11.4.E29] || [[Item:Q3961|<math>\deriv{}{z}\left(z^{\nu}\modStruveL{\nu}@{z}\right) = z^{\nu}\modStruveL{\nu-1}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\left(z^{\nu}\modStruveL{\nu}@{z}\right) = z^{\nu}\modStruveL{\nu-1}@{z}</syntaxhighlight> || <math>\realpart@@{n+\nu+\tfrac{3}{2}} > 0, \realpart@@{n+\nu-1+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>diff((z)^(nu)* StruveL(nu, z), z) = (z)^(nu)* StruveL(nu - 1, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[(z)^\[Nu]* StruveL[\[Nu], z], z] == (z)^\[Nu]* StruveL[\[Nu]- 1, z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 70] || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4.E30 11.4.E30] || [[Item:Q3962|<math>\deriv{}{z}\left(z^{-\nu}\modStruveL{\nu}@{z}\right) = \frac{2^{-\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}+z^{-\nu}\modStruveL{\nu+1}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\left(z^{-\nu}\modStruveL{\nu}@{z}\right) = \frac{2^{-\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}+z^{-\nu}\modStruveL{\nu+1}@{z}</syntaxhighlight> || <math>\realpart@@{\nu+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+1+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>diff((z)^(- nu)* StruveL(nu, z), z) = ((2)^(- nu))/(sqrt(Pi)*GAMMA(nu +(3)/(2)))+ (z)^(- nu)* StruveL(nu + 1, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[(z)^(- \[Nu])* StruveL[\[Nu], z], z] == Divide[(2)^(- \[Nu]),Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]]+ (z)^(- \[Nu])* StruveL[\[Nu]+ 1, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 56]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4#Ex1 11.4#Ex1] || [[Item:Q3964|<math>\StruveH{0}'@{z} = \frac{2}{\pi}-\StruveH{1}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{0}'@{z} = \frac{2}{\pi}-\StruveH{1}@{z}</syntaxhighlight> || <math>\realpart@@{n+0+\tfrac{3}{2}} > 0, \realpart@@{n+1+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>diff( StruveH(0, z), z$(1) ) = (2)/(Pi)- StruveH(1, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[StruveH[0, z], {z, 1}] == Divide[2,Pi]- StruveH[1, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4#Ex2 11.4#Ex2] || [[Item:Q3965|<math>\deriv{}{z}(z\StruveH{1}@{z}) = z\StruveH{0}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}(z\StruveH{1}@{z}) = z\StruveH{0}@{z}</syntaxhighlight> || <math>\realpart@@{n+1+\tfrac{3}{2}} > 0, \realpart@@{n+0+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>diff(z*StruveH(1, z), z) = z*StruveH(0, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[z*StruveH[1, z], z] == z*StruveH[0, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4#Ex3 11.4#Ex3] || [[Item:Q3966|<math>\modStruveL{0}'@{z} = \frac{2}{\pi}+\modStruveL{1}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveL{0}'@{z} = \frac{2}{\pi}+\modStruveL{1}@{z}</syntaxhighlight> || <math>\realpart@@{n+0+\tfrac{3}{2}} > 0, \realpart@@{n+1+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>diff( StruveL(0, z), z$(1) ) = (2)/(Pi)+ StruveL(1, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[StruveL[0, z], {z, 1}] == Divide[2,Pi]+ StruveL[1, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.4#Ex4 11.4#Ex4] || [[Item:Q3967|<math>\deriv{}{z}(z\modStruveL{1}@{z}) = z\modStruveL{0}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}(z\modStruveL{1}@{z}) = z\modStruveL{0}@{z}</syntaxhighlight> || <math>\realpart@@{n+1+\tfrac{3}{2}} > 0, \realpart@@{n+0+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>diff(z*StruveL(1, z), z) = z*StruveL(0, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[z*StruveL[1, z], z] == z*StruveL[0, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.5.E1 11.5.E1] || [[Item:Q3968|<math>\StruveH{\nu}@{z} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{1}(1-t^{2})^{\nu-\frac{1}{2}}\sin@{zt}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{\nu}@{z} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{1}(1-t^{2})^{\nu-\frac{1}{2}}\sin@{zt}\diff{t}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, \realpart@@{\nu+\tfrac{1}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(nu, z) = (2*((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* sin(z*t), t = 0..1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[\[Nu], z] == Divide[2*(Divide[1,2]*z)^\[Nu],Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Sin[z*t], {t, 0, 1}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 35]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.5.E1 11.5.E1] || [[Item:Q3968|<math>\frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{1}(1-t^{2})^{\nu-\frac{1}{2}}\sin@{zt}\diff{t} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\pi/2}\sin@{z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{1}(1-t^{2})^{\nu-\frac{1}{2}}\sin@{zt}\diff{t} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\pi/2}\sin@{z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, \realpart@@{\nu+\tfrac{1}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>(2*((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* sin(z*t), t = 0..1) = (2*((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))*int(sin(z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi/2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[2*(Divide[1,2]*z)^\[Nu],Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Sin[z*t], {t, 0, 1}, GenerateConditions->None] == Divide[2*(Divide[1,2]*z)^\[Nu],Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]*Integrate[Sin[z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi/2}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 35]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.5.E2 11.5.E2] || [[Item:Q3969|<math>\StruveK{\nu}@{z} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\infty}e^{-zt}(1+t^{2})^{\nu-\frac{1}{2}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveK{\nu}@{z} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\infty}e^{-zt}(1+t^{2})^{\nu-\frac{1}{2}}\diff{t}</syntaxhighlight> || <math>\realpart@@{z} > 0, \realpart@@{\nu+\tfrac{1}{2}} > 0, \realpart@@{\nu+k+1} > 0, \realpart@@{-\nu+k+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(nu, z) - BesselY(nu, z) = (2*((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))*int(exp(- z*t)*(1 + (t)^(2))^(nu -(1)/(2)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[\[Nu], z] - BesselY[\[Nu], z] == Divide[2*(Divide[1,2]*z)^\[Nu],Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*t]*(1 + (t)^(2))^(\[Nu]-Divide[1,2]), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [15 / 25]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.9495382353861556, -0.46093572348323536]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.7706973036767981, -0.20650772012904173]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.5.E3 11.5.E3] || [[Item:Q3970|<math>\StruveK{0}@{z} = \frac{2}{\pi}\int_{0}^{\infty}e^{-z\sinh@@{t}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveK{0}@{z} = \frac{2}{\pi}\int_{0}^{\infty}e^{-z\sinh@@{t}}\diff{t}</syntaxhighlight> || <math>\realpart@@{z} > 0, \realpart@@{0+k+1} > 0, \realpart@@{-0+k+1} > 0, \realpart@@{n+0+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(0, z) - BesselY(0, z) = (2)/(Pi)*int(exp(- z*sinh(t)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[0, z] - BesselY[0, z] == Divide[2,Pi]*Integrate[Exp[- z*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Aborted || - || Skipped - Because timed out
| |
| |-
| |
| | [https://dlmf.nist.gov/11.5.E4 11.5.E4] || [[Item:Q3971|<math>\modStruveM{\nu}@{z} = -\frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{1}e^{-zt}(1-t^{2})^{\nu-\frac{1}{2}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveM{\nu}@{z} = -\frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{1}e^{-zt}(1-t^{2})^{\nu-\frac{1}{2}}\diff{t}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, \realpart@@{\nu+\tfrac{1}{2}} > 0, \realpart@@{\nu+k+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveL(nu, z) - BesselI(nu, z) = -(2*((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))*int(exp(- z*t)*(1 - (t)^(2))^(nu -(1)/(2)), t = 0..1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[\[Nu], z] - BesselI[\[Nu], z] == -Divide[2*(Divide[1,2]*z)^\[Nu],Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*t]*(1 - (t)^(2))^(\[Nu]-Divide[1,2]), {t, 0, 1}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 35]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.5.E5 11.5.E5] || [[Item:Q3972|<math>\modStruveM{0}@{z} = -\frac{2}{\pi}\int_{0}^{\pi/2}e^{-z\cos@@{\theta}}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveM{0}@{z} = -\frac{2}{\pi}\int_{0}^{\pi/2}e^{-z\cos@@{\theta}}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{0+k+1} > 0, \realpart@@{n+0+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveL(0, z) - BesselI(0, z) = -(2)/(Pi)*int(exp(- z*cos(theta)), theta = 0..Pi/2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[0, z] - BesselI[0, z] == -Divide[2,Pi]*Integrate[Exp[- z*Cos[\[Theta]]], {\[Theta], 0, Pi/2}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.5.E6 11.5.E6] || [[Item:Q3973|<math>\modStruveL{\nu}@{z} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\pi/2}\sinh@{z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveL{\nu}@{z} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\pi/2}\sinh@{z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, \realpart@@{\nu+\tfrac{1}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>StruveL(nu, z) = (2*((1)/(2)*z)^(nu))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))*int(sinh(z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi/2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[\[Nu], z] == Divide[2*(Divide[1,2]*z)^\[Nu],Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]*Integrate[Sinh[z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi/2}, GenerateConditions->None]</syntaxhighlight> || Successful || Aborted || - || Skipped - Because timed out
| |
| |-
| |
| | [https://dlmf.nist.gov/11.5.E7 11.5.E7] || [[Item:Q3974|<math>\modBesselI{-\nu}@{x}-\modStruveL{\nu}@{x} = \frac{2(\tfrac{1}{2}x)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\infty}(1+t^{2})^{\nu-\frac{1}{2}}\sin@{xt}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{-\nu}@{x}-\modStruveL{\nu}@{x} = \frac{2(\tfrac{1}{2}x)^{\nu}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\infty}(1+t^{2})^{\nu-\frac{1}{2}}\sin@{xt}\diff{t}</syntaxhighlight> || <math>x > 0, \realpart@@{\nu+\tfrac{1}{2}} > 0, \realpart@@{-\nu+k+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(- nu, x)- StruveL(nu, x) = (2*((1)/(2)*x)^(nu))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))*int((1 + (t)^(2))^(nu -(1)/(2))* sin(x*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[- \[Nu], x]- StruveL[\[Nu], x] == Divide[2*(Divide[1,2]*x)^\[Nu],Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 + (t)^(2))^(\[Nu]-Divide[1,2])* Sin[x*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.291209379
| |
| Test Values: {x = 3/2, nu = 0}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.709400861
| |
| Test Values: {x = 1/2, nu = 0}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
| |
| |-
| |
| | [https://dlmf.nist.gov/11.5.E8 11.5.E8] || [[Item:Q3975|<math>(\tfrac{1}{2}x)^{-\nu-1}\StruveH{\nu}@{x} = -\frac{1}{2\pi i}\int_{-i\infty}^{i\infty}\frac{\pi\csc@{\pi s}}{\EulerGamma@{\tfrac{3}{2}+s}\EulerGamma@{\tfrac{3}{2}+\nu+s}}(\tfrac{1}{4}x^{2})^{s}\diff{s}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(\tfrac{1}{2}x)^{-\nu-1}\StruveH{\nu}@{x} = -\frac{1}{2\pi i}\int_{-i\infty}^{i\infty}\frac{\pi\csc@{\pi s}}{\EulerGamma@{\tfrac{3}{2}+s}\EulerGamma@{\tfrac{3}{2}+\nu+s}}(\tfrac{1}{4}x^{2})^{s}\diff{s}</syntaxhighlight> || <math>x > 0, \realpart@@{\nu} > -1, \realpart@@{\tfrac{3}{2}+s} > 0, \realpart@@{\tfrac{3}{2}+\nu+s} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>((1)/(2)*x)^(- nu - 1)* StruveH(nu, x) = -(1)/(2*Pi*I)*int((Pi*csc(Pi*s))/(GAMMA((3)/(2)+ s)*GAMMA((3)/(2)+ nu + s))*((1)/(4)*(x)^(2))^(s), s = - I*infinity..I*infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Divide[1,2]*x)^(- \[Nu]- 1)* StruveH[\[Nu], x] == -Divide[1,2*Pi*I]*Integrate[Divide[Pi*Csc[Pi*s],Gamma[Divide[3,2]+ s]*Gamma[Divide[3,2]+ \[Nu]+ s]]*(Divide[1,4]*(x)^(2))^(s), {s, - I*Infinity, I*Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
| |
| |-
| |
| | [https://dlmf.nist.gov/11.5.E9 11.5.E9] || [[Item:Q3976|<math>(\tfrac{1}{2}z)^{-\nu-1}\modStruveL{\nu}@{z} = \frac{1}{2\pi i}\int_{\infty}^{(0+)}\frac{\pi\csc@{\pi s}}{\EulerGamma@{\tfrac{3}{2}+s}\EulerGamma@{\tfrac{3}{2}+\nu+s}}(-\tfrac{1}{4}z^{2})^{s}\diff{s}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(\tfrac{1}{2}z)^{-\nu-1}\modStruveL{\nu}@{z} = \frac{1}{2\pi i}\int_{\infty}^{(0+)}\frac{\pi\csc@{\pi s}}{\EulerGamma@{\tfrac{3}{2}+s}\EulerGamma@{\tfrac{3}{2}+\nu+s}}(-\tfrac{1}{4}z^{2})^{s}\diff{s}</syntaxhighlight> || <math>\realpart@@{\tfrac{3}{2}+s} > 0, \realpart@@{\tfrac{3}{2}+\nu+s} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>((1)/(2)*z)^(- nu - 1)* StruveL(nu, z) = (1)/(2*Pi*I)*int((Pi*csc(Pi*s))/(GAMMA((3)/(2)+ s)*GAMMA((3)/(2)+ nu + s))*(-(1)/(4)*(z)^(2))^(s), s = infinity..(0 +))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Divide[1,2]*z)^(- \[Nu]- 1)* StruveL[\[Nu], z] == Divide[1,2*Pi*I]*Integrate[Divide[Pi*Csc[Pi*s],Gamma[Divide[3,2]+ s]*Gamma[Divide[3,2]+ \[Nu]+ s]]*(-Divide[1,4]*(z)^(2))^(s), {s, Infinity, (0 +)}, GenerateConditions->None]</syntaxhighlight> || Error || Failure || - || Error
| |
| |-
| |
| | [https://dlmf.nist.gov/11.6#Ex1 11.6#Ex1] || [[Item:Q3984|<math>c_{0}(\lambda) = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>c_{0}(\lambda) = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>c[0](lambda) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[c, 0][\[Lambda]] == 1</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.6#Ex2 11.6#Ex2] || [[Item:Q3985|<math>c_{1}(\lambda) = 2\lambda^{-2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>c_{1}(\lambda) = 2\lambda^{-2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>c[1](lambda) = 2*(lambda)^(- 2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[c, 1][\[Lambda]] == 2*\[Lambda]^(- 2)</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.6#Ex3 11.6#Ex3] || [[Item:Q3986|<math>c_{2}(\lambda) = 6\lambda^{-4}-\tfrac{1}{2}\lambda^{-2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>c_{2}(\lambda) = 6\lambda^{-4}-\tfrac{1}{2}\lambda^{-2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>c[2](lambda) = 6*(lambda)^(- 4)-(1)/(2)*(lambda)^(- 2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[c, 2][\[Lambda]] == 6*\[Lambda]^(- 4)-Divide[1,2]*\[Lambda]^(- 2)</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.6#Ex4 11.6#Ex4] || [[Item:Q3987|<math>c_{3}(\lambda) = 20\lambda^{-6}-4\lambda^{-4}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>c_{3}(\lambda) = 20\lambda^{-6}-4\lambda^{-4}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>c[3](lambda) = 20*(lambda)^(- 6)- 4*(lambda)^(- 4)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[c, 3][\[Lambda]] == 20*\[Lambda]^(- 6)- 4*\[Lambda]^(- 4)</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.6#Ex5 11.6#Ex5] || [[Item:Q3988|<math>c_{4}(\lambda) = 70\lambda^{-8}-\tfrac{45}{2}\lambda^{-6}+\tfrac{3}{8}\lambda^{-4}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>c_{4}(\lambda) = 70\lambda^{-8}-\tfrac{45}{2}\lambda^{-6}+\tfrac{3}{8}\lambda^{-4}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>c[4](lambda) = 70*(lambda)^(- 8)-(45)/(2)*(lambda)^(- 6)+(3)/(8)*(lambda)^(- 4)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[c, 4][\[Lambda]] == 70*\[Lambda]^(- 8)-Divide[45,2]*\[Lambda]^(- 6)+Divide[3,8]*\[Lambda]^(- 4)</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7.E1 11.7.E1] || [[Item:Q3990|<math>\int z^{\nu}\StruveH{\nu-1}@{z}\diff{z} = z^{\nu}\StruveH{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int z^{\nu}\StruveH{\nu-1}@{z}\diff{z} = z^{\nu}\StruveH{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{n+\nu-1+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>int((z)^(nu)* StruveH(nu - 1, z), z) = (z)^(nu)* StruveH(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(z)^\[Nu]* StruveH[\[Nu]- 1, z], z, GenerateConditions->None] == (z)^\[Nu]* StruveH[\[Nu], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7.E2 11.7.E2] || [[Item:Q3991|<math>\int z^{-\nu}\StruveH{\nu+1}@{z}\diff{z} = -z^{-\nu}\StruveH{\nu}@{z}+\frac{2^{-\nu}z}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int z^{-\nu}\StruveH{\nu+1}@{z}\diff{z} = -z^{-\nu}\StruveH{\nu}@{z}+\frac{2^{-\nu}z}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}</syntaxhighlight> || <math>\realpart@@{\nu+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+1+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>int((z)^(- nu)* StruveH(nu + 1, z), z) = - (z)^(- nu)* StruveH(nu, z)+((2)^(- nu)* z)/(sqrt(Pi)*GAMMA(nu +(3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(z)^(- \[Nu])* StruveH[\[Nu]+ 1, z], z, GenerateConditions->None] == - (z)^(- \[Nu])* StruveH[\[Nu], z]+Divide[(2)^(- \[Nu])* z,Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 56]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7.E3 11.7.E3] || [[Item:Q3992|<math>\int z^{\nu}\modStruveL{\nu-1}@{z}\diff{z} = z^{\nu}\modStruveL{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int z^{\nu}\modStruveL{\nu-1}@{z}\diff{z} = z^{\nu}\modStruveL{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{n+\nu-1+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>int((z)^(nu)* StruveL(nu - 1, z), z) = (z)^(nu)* StruveL(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(z)^\[Nu]* StruveL[\[Nu]- 1, z], z, GenerateConditions->None] == (z)^\[Nu]* StruveL[\[Nu], z]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 15.74633170+6.711214442*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1573.901952-547.1907270*I
| |
| Test Values: {nu = -1/2+1/2*I*3^(1/2), z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7.E4 11.7.E4] || [[Item:Q3993|<math>\int z^{-\nu}\modStruveL{\nu+1}@{z}\diff{z} = z^{-\nu}\modStruveL{\nu}@{z}-\frac{2^{-\nu}z}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int z^{-\nu}\modStruveL{\nu+1}@{z}\diff{z} = z^{-\nu}\modStruveL{\nu}@{z}-\frac{2^{-\nu}z}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}</syntaxhighlight> || <math>\realpart@@{\nu+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+1+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>int((z)^(- nu)* StruveL(nu + 1, z), z) = (z)^(- nu)* StruveL(nu, z)-((2)^(- nu)* z)/(sqrt(Pi)*GAMMA(nu +(3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(z)^(- \[Nu])* StruveL[\[Nu]+ 1, z], z, GenerateConditions->None] == (z)^(- \[Nu])* StruveL[\[Nu], z]-Divide[(2)^(- \[Nu])* z,Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 56]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7.E5 11.7.E5] || [[Item:Q3994|<math>f_{\nu}(z) = \int_{0}^{z}t^{\nu}\StruveH{\nu}@{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>f_{\nu}(z) = \int_{0}^{z}t^{\nu}\StruveH{\nu}@{t}\diff{t}</syntaxhighlight> || <math>\realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>f[nu](z) = int((t)^(nu)* StruveH(nu, t), t = 0..z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[f, \[Nu]][z] == Integrate[(t)^\[Nu]* StruveH[\[Nu], t], {t, 0, z}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .4776177026+.8322237517*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[nu] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.8884077018+.4661983481*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[nu] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.4776177021895665, 0.8322237514648603]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.8884077015948724, 0.4661983476804216]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7.E6 11.7.E6] || [[Item:Q3995|<math>f_{\nu+1}(z) = (2\nu+1)f_{\nu}(z)-z^{\nu+1}\StruveH{\nu}@{z}+\frac{(\tfrac{1}{2}z^{2})^{\nu+1}}{(\nu+1)\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>f_{\nu+1}(z) = (2\nu+1)f_{\nu}(z)-z^{\nu+1}\StruveH{\nu}@{z}+\frac{(\tfrac{1}{2}z^{2})^{\nu+1}}{(\nu+1)\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}</syntaxhighlight> || <math>\realpart@@{\nu} > -1, \realpart@@{\nu+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>f[nu + 1](z) = (2*nu + 1)*f[nu](z)- (z)^(nu + 1)* StruveH(nu, z)+(((1)/(2)*(z)^(2))^(nu + 1))/((nu + 1)*sqrt(Pi)*GAMMA(nu +(3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[f, \[Nu]+ 1][z] == (2*\[Nu]+ 1)*Subscript[f, \[Nu]][z]- (z)^(\[Nu]+ 1)* StruveH[\[Nu], z]+Divide[(Divide[1,2]*(z)^(2))^(\[Nu]+ 1),(\[Nu]+ 1)*Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2926898254e-1-1.890529289*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[nu] = 1/2*3^(1/2)+1/2*I, f[nu+1] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.336756421-2.256554693*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[nu] = 1/2*3^(1/2)+1/2*I, f[nu+1] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.029268983232513014, -1.8905292888907776]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.3367564205519258, -2.2565546926752162]
| |
| Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[1, ν]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7.E7 11.7.E7] || [[Item:Q3996|<math>\int_{0}^{\pi/2}\StruveH{\nu}@{z\sin@@{\theta}}\frac{(\sin@@{\theta})^{\nu+1}}{(\cos@@{\theta})^{2\nu}}\diff{\theta} = \frac{2^{-\nu}}{\sqrt{\pi}}\EulerGamma@{\tfrac{1}{2}-\nu}z^{\nu-1}(1-\cos@@{z})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\pi/2}\StruveH{\nu}@{z\sin@@{\theta}}\frac{(\sin@@{\theta})^{\nu+1}}{(\cos@@{\theta})^{2\nu}}\diff{\theta} = \frac{2^{-\nu}}{\sqrt{\pi}}\EulerGamma@{\tfrac{1}{2}-\nu}z^{\nu-1}(1-\cos@@{z})</syntaxhighlight> || <math>-\tfrac{3}{2} < \realpart@@{\nu}, \realpart@@{\nu} < \tfrac{1}{2}, \realpart@@{\tfrac{1}{2}-\nu} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>int(StruveH(nu, z*sin(theta))*((sin(theta))^(nu + 1))/((cos(theta))^(2*nu)), theta = 0..Pi/2) = ((2)^(- nu))/(sqrt(Pi))*GAMMA((1)/(2)- nu)*(z)^(nu - 1)*(1 - cos(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[StruveH[\[Nu], z*Sin[\[Theta]]]*Divide[(Sin[\[Theta]])^(\[Nu]+ 1),(Cos[\[Theta]])^(2*\[Nu])], {\[Theta], 0, Pi/2}, GenerateConditions->None] == Divide[(2)^(- \[Nu]),Sqrt[Pi]]*Gamma[Divide[1,2]- \[Nu]]*(z)^(\[Nu]- 1)*(1 - Cos[z])</syntaxhighlight> || Successful || Aborted || - || Successful [Tested: 21]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7#Ex1 11.7#Ex1] || [[Item:Q3997|<math>\int_{0}^{\infty}\StruveH{0}@{t}\,\frac{\diff{t}}{t} = \tfrac{1}{2}\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\StruveH{0}@{t}\,\frac{\diff{t}}{t} = \tfrac{1}{2}\pi</syntaxhighlight> || <math>\realpart@@{n+0+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>int(StruveH(0, t)*(1)/(t), t = 0..infinity) = (1)/(2)*Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[StruveH[0, t]*Divide[1,t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,2]*Pi</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7#Ex2 11.7#Ex2] || [[Item:Q3998|<math>\int_{0}^{\infty}\StruveH{1}@{t}\,\frac{\diff{t}}{t^{2}} = \tfrac{1}{4}\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\StruveH{1}@{t}\,\frac{\diff{t}}{t^{2}} = \tfrac{1}{4}\pi</syntaxhighlight> || <math>\realpart@@{n+1+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>int(StruveH(1, t)*(1)/((t)^(2)), t = 0..infinity) = (1)/(4)*Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[StruveH[1, t]*Divide[1,(t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,4]*Pi</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7.E9 11.7.E9] || [[Item:Q3999|<math>\int_{0}^{\infty}\StruveH{\nu}@{t}\diff{t} = -\cot@{\tfrac{1}{2}\pi\nu}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\StruveH{\nu}@{t}\diff{t} = -\cot@{\tfrac{1}{2}\pi\nu}</syntaxhighlight> || <math>-2 < \realpart@@{\nu}, \realpart@@{\nu} < 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>int(StruveH(nu, t), t = 0..infinity) = - cot((1)/(2)*Pi*nu)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[StruveH[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == - Cot[Divide[1,2]*Pi*\[Nu]]</syntaxhighlight> || Successful || Aborted || - || Successful [Tested: 4]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7.E10 11.7.E10] || [[Item:Q4000|<math>\int_{0}^{\infty}t^{-\nu-1}\StruveH{\nu}@{t}\diff{t} = \frac{\pi}{2^{\nu+1}\EulerGamma@{\nu+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}t^{-\nu-1}\StruveH{\nu}@{t}\diff{t} = \frac{\pi}{2^{\nu+1}\EulerGamma@{\nu+1}}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{3}{2}, \realpart@@{\nu+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>int((t)^(- nu - 1)* StruveH(nu, t), t = 0..infinity) = (Pi)/((2)^(nu + 1)* GAMMA(nu + 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(t)^(- \[Nu]- 1)* StruveH[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Pi,(2)^(\[Nu]+ 1)* Gamma[\[Nu]+ 1]]</syntaxhighlight> || Successful || Aborted || - || Skipped - Because timed out
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7.E11 11.7.E11] || [[Item:Q4001|<math>\int_{0}^{\infty}t^{\mu-\nu-1}\StruveH{\nu}@{t}\diff{t} = \frac{\EulerGamma@{\tfrac{1}{2}\mu}2^{\mu-\nu-1}\tan@{\tfrac{1}{2}\pi\mu}}{\EulerGamma@{\nu-\tfrac{1}{2}\mu+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}t^{\mu-\nu-1}\StruveH{\nu}@{t}\diff{t} = \frac{\EulerGamma@{\tfrac{1}{2}\mu}2^{\mu-\nu-1}\tan@{\tfrac{1}{2}\pi\mu}}{\EulerGamma@{\nu-\tfrac{1}{2}\mu+1}}</syntaxhighlight> || <math>|\realpart@@{\mu}| < 1, \realpart@@{\nu} > \realpart@@{\mu}-\tfrac{3}{2}, \realpart@@{\tfrac{1}{2}\mu} > 0, \realpart@@{\nu-\tfrac{1}{2}\mu+1} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>int((t)^(mu - nu - 1)* StruveH(nu, t), t = 0..infinity) = (GAMMA((1)/(2)*mu)*(2)^(mu - nu - 1)* tan((1)/(2)*Pi*mu))/(GAMMA(nu -(1)/(2)*mu + 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(t)^(\[Mu]- \[Nu]- 1)* StruveH[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[Divide[1,2]*\[Mu]]*(2)^(\[Mu]- \[Nu]- 1)* Tan[Divide[1,2]*Pi*\[Mu]],Gamma[\[Nu]-Divide[1,2]*\[Mu]+ 1]]</syntaxhighlight> || Successful || Aborted || - || Skipped - Because timed out
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7.E12 11.7.E12] || [[Item:Q4002|<math>\int_{0}^{\infty}t^{-\mu-\nu}\StruveH{\mu}@{t}\StruveH{\nu}@{t}\diff{t} = \frac{\sqrt{\pi}\EulerGamma@{\mu+\nu}}{2^{\mu+\nu}\EulerGamma@{\mu+\nu+\tfrac{1}{2}}\EulerGamma@{\mu+\tfrac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}t^{-\mu-\nu}\StruveH{\mu}@{t}\StruveH{\nu}@{t}\diff{t} = \frac{\sqrt{\pi}\EulerGamma@{\mu+\nu}}{2^{\mu+\nu}\EulerGamma@{\mu+\nu+\tfrac{1}{2}}\EulerGamma@{\mu+\tfrac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}</syntaxhighlight> || <math>\realpart@{\mu+\nu} > 0, \realpart@@{\mu+\nu} > 0, \realpart@@{\mu+\nu+\tfrac{1}{2}} > 0, \realpart@@{\mu+\tfrac{1}{2}} > 0, \realpart@@{\nu+\tfrac{1}{2}} > 0, \realpart@@{n+\mu+\tfrac{3}{2}} > 0, \realpart@@{n+\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>int((t)^(- mu - nu)* StruveH(mu, t)*StruveH(nu, t), t = 0..infinity) = (sqrt(Pi)*GAMMA(mu + nu))/((2)^(mu + nu)* GAMMA(mu + nu +(1)/(2))*GAMMA(mu +(1)/(2))*GAMMA(nu +(1)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(t)^(- \[Mu]- \[Nu])* StruveH[\[Mu], t]*StruveH[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Sqrt[Pi]*Gamma[\[Mu]+ \[Nu]],(2)^(\[Mu]+ \[Nu])* Gamma[\[Mu]+ \[Nu]+Divide[1,2]]*Gamma[\[Mu]+Divide[1,2]]*Gamma[\[Nu]+Divide[1,2]]]</syntaxhighlight> || Successful || Aborted || - || Skipped - Because timed out
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7.E13 11.7.E13] || [[Item:Q4003|<math>\int_{0}^{\infty}e^{-at}\StruveH{0}@{t}\diff{t} = \frac{2}{\pi\sqrt{1+a^{2}}}\ln@{\frac{1+\sqrt{1+a^{2}}}{a}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}e^{-at}\StruveH{0}@{t}\diff{t} = \frac{2}{\pi\sqrt{1+a^{2}}}\ln@{\frac{1+\sqrt{1+a^{2}}}{a}}</syntaxhighlight> || <math>\realpart@@{n+0+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>int(exp(- a*t)*StruveH(0, t), t = 0..infinity) = (2)/(Pi*sqrt(1 + (a)^(2)))*ln((1 +sqrt(1 + (a)^(2)))/(a))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[- a*t]*StruveH[0, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[2,Pi*Sqrt[1 + (a)^(2)]]*Log[Divide[1 +Sqrt[1 + (a)^(2)],a]]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0.-1.109400392*I
| |
| Test Values: {a = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .7e-9-1.788854381*I
| |
| Test Values: {a = -1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-8.326672684688674*^-17, -1.1094003924504583]
| |
| Test Values: {Rule[a, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.0, -1.7888543819998317]
| |
| Test Values: {Rule[a, -0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7.E14 11.7.E14] || [[Item:Q4004|<math>\int_{0}^{\infty}e^{-at}\StruveH{1}@{t}\diff{t} = \frac{2}{\pi a}-\frac{2a}{\pi\sqrt{1+a^{2}}}\ln@{\frac{1+\sqrt{1+a^{2}}}{a}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}e^{-at}\StruveH{1}@{t}\diff{t} = \frac{2}{\pi a}-\frac{2a}{\pi\sqrt{1+a^{2}}}\ln@{\frac{1+\sqrt{1+a^{2}}}{a}}</syntaxhighlight> || <math>\realpart@@{n+1+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>int(exp(- a*t)*StruveH(1, t), t = 0..infinity) = (2)/(Pi*a)-(2*a)/(Pi*sqrt(1 + (a)^(2)))*ln((1 +sqrt(1 + (a)^(2)))/(a))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[- a*t]*StruveH[1, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[2,Pi*a]-Divide[2*a,Pi*Sqrt[1 + (a)^(2)]]*Log[Divide[1 +Sqrt[1 + (a)^(2)],a]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1865480398-1.664100588*I
| |
| Test Values: {a = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.724458563-.8944271906*I
| |
| Test Values: {a = -1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-5.551115123125783*^-17, -1.6641005886756874]
| |
| Test Values: {Rule[a, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.1102230246251565*^-16, -0.8944271909999159]
| |
| Test Values: {Rule[a, -0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7.E15 11.7.E15] || [[Item:Q4005|<math>\int_{0}^{\infty}e^{-at}\modStruveL{0}@{t}\diff{t} = \frac{2}{\pi\sqrt{a^{2}\!-\!1}}\asin@{\frac{1}{a}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}e^{-at}\modStruveL{0}@{t}\diff{t} = \frac{2}{\pi\sqrt{a^{2}\!-\!1}}\asin@{\frac{1}{a}}</syntaxhighlight> || <math>\realpart@@{n+0+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>int(exp(- a*t)*StruveL(0, t), t = 0..infinity) = (2)/(Pi*sqrt((a)^(2)- 1))*arcsin((1)/(a))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[- a*t]*StruveL[0, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[2,Pi*Sqrt[(a)^(2)- 1]]*ArcSin[Divide[1,a]]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8310285000-.2578603735e-9*I
| |
| Test Values: {a = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.936205180+0.*I
| |
| Test Values: {a = -1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 6]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.7#Ex4 11.7#Ex4] || [[Item:Q4007|<math> = \frac{2a}{\pi\sqrt{a^{2}\!-\!1}}\atan@{\frac{1}{\sqrt{a^{2}\!-\!1}}}-\frac{2}{\pi a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline> = \frac{2a}{\pi\sqrt{a^{2}\!-\!1}}\atan@{\frac{1}{\sqrt{a^{2}\!-\!1}}}-\frac{2}{\pi a}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>= (2*a)/(Pi*sqrt((a)^(2)- 1))*arctan((1)/(sqrt((a)^(2)- 1)))-(2)/(Pi*a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>== Divide[2*a,Pi*Sqrt[(a)^(2)- 1]]*ArcTan[Divide[1,Sqrt[(a)^(2)- 1]]]-Divide[2,Pi*a]</syntaxhighlight> || Error || Failure || - || Error
| |
| |-
| |
| | [https://dlmf.nist.gov/11.9.E1 11.9.E1] || [[Item:Q4008|<math>\deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}+\left(1-\frac{\nu^{2}}{z^{2}}\right)w = z^{\mu-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}+\left(1-\frac{\nu^{2}}{z^{2}}\right)w = z^{\mu-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)])+(1)/(z)*diff(w, z)+(1 -((nu)^(2))/((z)^(2)))*w = (z)^(mu - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}]+Divide[1,z]*D[w, z]+(1 -Divide[\[Nu]^(2),(z)^(2)])*w == (z)^(\[Mu]- 1)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.7677724761+.5394693872e-1*I
| |
| Test Values: {mu = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.394855253+1.097179568*I
| |
| Test Values: {mu = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.7677724760456721, 0.053946938885231305]
| |
| Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.9642783315232053, 1.0539469388852312]
| |
| Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.9.E2 11.9.E2] || [[Item:Q4009|<math>w = \Lommels{\mu}{\nu}@{z}+A\BesselJ{\nu}@{z}+B\BesselY{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \Lommels{\mu}{\nu}@{z}+A\BesselJ{\nu}@{z}+B\BesselY{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{\nu+k+1} > 0, \realpart@@{-\nu+k+1} > 0</math> || <syntaxhighlight lang=mathematica>w = LommelS1(mu, nu, z)+ A*BesselJ(nu, z)+ B*BesselY(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .9752372341+.4710119144*I
| |
| Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.486411080-.4774576789*I
| |
| Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.9.E3 11.9.E3] || [[Item:Q4010|<math>\Lommels{\mu}{\nu}@{z} = z^{\mu+1}\sum_{k=0}^{\infty}(-1)^{k}\frac{z^{2k}}{a_{k+1}(\mu,\nu)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Lommels{\mu}{\nu}@{z} = z^{\mu+1}\sum_{k=0}^{\infty}(-1)^{k}\frac{z^{2k}}{a_{k+1}(\mu,\nu)}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LommelS1(mu, nu, z) = (z)^(mu + 1)* sum((- 1)^(k)*((z)^(2*k))/(a[k + 1](mu , nu)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Error || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.9.E4 11.9.E4] || [[Item:Q4011|<math>a_{k}(\mu,\nu) = \prod_{m=1}^{k}\left((\mu+2m-1)^{2}-\nu^{2}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>a_{k}(\mu,\nu) = \prod_{m=1}^{k}\left((\mu+2m-1)^{2}-\nu^{2}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>a[k](mu , nu) = product((mu + 2*m - 1)^(2)- (nu)^(2), m = 1..k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[a, k][\[Mu], \[Nu]] == Product[(\[Mu]+ 2*m - 1)^(2)- \[Nu]^(2), {m, 1, k}, GenerateConditions->None]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.9.E5 11.9.E5] || [[Item:Q4012|<math>\LommelS{\mu}{\nu}@{z} = \Lommels{\mu}{\nu}@{z}+2^{\mu-1}\EulerGamma@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}}\EulerGamma@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu+\tfrac{1}{2}}\*\left(\sin@{\tfrac{1}{2}(\mu-\nu)\pi}\,\BesselJ{\nu}@{z}-\cos@{\tfrac{1}{2}(\mu-\nu)\pi}\,\BesselY{\nu}@{z}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\LommelS{\mu}{\nu}@{z} = \Lommels{\mu}{\nu}@{z}+2^{\mu-1}\EulerGamma@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}}\EulerGamma@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu+\tfrac{1}{2}}\*\left(\sin@{\tfrac{1}{2}(\mu-\nu)\pi}\,\BesselJ{\nu}@{z}-\cos@{\tfrac{1}{2}(\mu-\nu)\pi}\,\BesselY{\nu}@{z}\right)</syntaxhighlight> || <math>\realpart@@{\nu+k+1} > 0, \realpart@@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}} > 0, \realpart@@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu+\tfrac{1}{2}} > 0, \realpart@@{-\nu+k+1} > 0</math> || <syntaxhighlight lang=mathematica>LommelS2(mu, nu, z) = LommelS1(mu, nu, z)+ (2)^(mu - 1)* GAMMA((1)/(2)*mu +(1)/(2)*nu +(1)/(2))*GAMMA((1)/(2)*mu -(1)/(2)*nu +(1)/(2))*(sin((1)/(2)*(mu - nu)*Pi)*BesselJ(nu, z)- cos((1)/(2)*(mu - nu)*Pi)*BesselY(nu, z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.9#Ex1 11.9#Ex1] || [[Item:Q4013|<math>\Lommels{\mu}{-\nu}@{z} = \Lommels{\mu}{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Lommels{\mu}{-\nu}@{z} = \Lommels{\mu}{\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LommelS1(mu, - nu, z) = LommelS1(mu, nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.9#Ex2 11.9#Ex2] || [[Item:Q4014|<math>\LommelS{\mu}{-\nu}@{z} = \LommelS{\mu}{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\LommelS{\mu}{-\nu}@{z} = \LommelS{\mu}{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{-\nu+k+1} > 0, \realpart@@{\nu+k+1} > 0, \realpart@@{\tfrac{1}{2}\mu+\tfrac{1}{2}-\nu+\tfrac{1}{2}} > 0, \realpart@@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}} > 0, \realpart@@{\tfrac{1}{2}\mu-\tfrac{1}{2}-\nu+\tfrac{1}{2}} > 0, \realpart@@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu+\tfrac{1}{2}} > 0, \realpart@@{--\nu+k+1} > 0</math> || <syntaxhighlight lang=mathematica>LommelS2(mu, - nu, z) = LommelS2(mu, nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.9.E7 11.9.E7] || [[Item:Q4015|<math>\Lommels{\mu}{\nu}@{z} = 2^{\mu+1}\sum_{k=0}^{\infty}\*\frac{(2k+\mu+1)\EulerGamma@{k+\mu+1}}{k!(2k+\mu-\nu+1)(2k+\mu+\nu+1)}\BesselJ{2k+\mu+1}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Lommels{\mu}{\nu}@{z} = 2^{\mu+1}\sum_{k=0}^{\infty}\*\frac{(2k+\mu+1)\EulerGamma@{k+\mu+1}}{k!(2k+\mu-\nu+1)(2k+\mu+\nu+1)}\BesselJ{2k+\mu+1}@{z}</syntaxhighlight> || <math>\realpart@@{2k+\mu+1+k+1} > 0, \realpart@@{k+\mu+1} > 0</math> || <syntaxhighlight lang=mathematica>LommelS1(mu, nu, z) = (2)^(mu + 1)* sum(*((2*k + mu + 1)*GAMMA(k + mu + 1))/(factorial(k)*(2*k + mu - nu + 1)*(2*k + mu + nu + 1))*BesselJ(2*k + mu + 1, z), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Error || Missing Macro Error || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.9.E8 11.9.E8] || [[Item:Q4016|<math>\Lommels{\mu}{\nu}@{z} = 2^{(\mu+\nu-1)/2}\EulerGamma@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}}z^{(\mu+1-\nu)/2}\*\sum_{k=0}^{\infty}\frac{(\tfrac{1}{2}z)^{k}}{k!(2k+\mu-\nu+1)}\BesselJ{k+\frac{1}{2}(\mu+\nu+1)}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Lommels{\mu}{\nu}@{z} = 2^{(\mu+\nu-1)/2}\EulerGamma@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}}z^{(\mu+1-\nu)/2}\*\sum_{k=0}^{\infty}\frac{(\tfrac{1}{2}z)^{k}}{k!(2k+\mu-\nu+1)}\BesselJ{k+\frac{1}{2}(\mu+\nu+1)}@{z}</syntaxhighlight> || <math>\realpart@@{k+\frac{1}{2}(\mu+\nu+1)+k+1} > 0, \realpart@@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}} > 0</math> || <syntaxhighlight lang=mathematica>LommelS1(mu, nu, z) = (2)^((mu + nu - 1)/2)* GAMMA((1)/(2)*mu +(1)/(2)*nu +(1)/(2))*(z)^((mu + 1 - nu)/2)* sum((((1)/(2)*z)^(k))/(factorial(k)*(2*k + mu - nu + 1))*BesselJ(k +(1)/(2)*(mu + nu + 1), z), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Skipped - Because timed out || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E1 11.10.E1] || [[Item:Q4018|<math>\AngerJ{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{\nu\theta-z\sin@@{\theta}}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{\nu\theta-z\sin@@{\theta}}\diff{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(nu, z) = (1)/(Pi)*int(cos(nu*theta - z*sin(theta)), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[\[Nu], z] == Divide[1,Pi]*Integrate[Cos[\[Nu]*\[Theta]- z*Sin[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 70] || Skipped - Because timed out
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E2 11.10.E2] || [[Item:Q4019|<math>\WeberE{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\sin@{\nu\theta-z\sin@@{\theta}}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\sin@{\nu\theta-z\sin@@{\theta}}\diff{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE(nu, z) = (1)/(Pi)*int(sin(nu*theta - z*sin(theta)), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[\[Nu], z] == Divide[1,Pi]*Integrate[Sin[\[Nu]*\[Theta]- z*Sin[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 70] || Skipped - Because timed out
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E3 11.10.E3] || [[Item:Q4020|<math>\frac{1}{\pi}\int_{0}^{2\pi}\cos@{\nu\theta-z\sin@@{\theta}}\diff{\theta} = (1+\cos@{2\pi\nu})\,\AngerJ{\nu}@{z}+\sin@{2\pi\nu}\WeberE{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{\pi}\int_{0}^{2\pi}\cos@{\nu\theta-z\sin@@{\theta}}\diff{\theta} = (1+\cos@{2\pi\nu})\,\AngerJ{\nu}@{z}+\sin@{2\pi\nu}\WeberE{\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(Pi)*int(cos(nu*theta - z*sin(theta)), theta = 0..2*Pi) = (1 + cos(2*Pi*nu))*AngerJ(nu, z)+ sin(2*Pi*nu)*WeberE(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,Pi]*Integrate[Cos[\[Nu]*\[Theta]- z*Sin[\[Theta]]], {\[Theta], 0, 2*Pi}, GenerateConditions->None] == (1 + Cos[2*Pi*\[Nu]])*AngerJ[\[Nu], z]+ Sin[2*Pi*\[Nu]]*WeberE[\[Nu], z]</syntaxhighlight> || Failure || Failure || Successful [Tested: 70] || Skipped - Because timed out
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E8 11.10.E8] || [[Item:Q4025|<math>\AngerJ{\nu}@{z} = \cos@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)+\sin@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\nu}@{z} = \cos@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)+\sin@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(nu, z) = cos((1)/(2)*Pi*nu)*S[1](nu , z)+ sin((1)/(2)*Pi*nu)*S[2](nu , z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[\[Nu], z] == Cos[Divide[1,2]*Pi*\[Nu]]*Subscript[S, 1][\[Nu], z]+ Sin[Divide[1,2]*Pi*\[Nu]]*Subscript[S, 2][\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .4325617835-.4216939044*I-(1.695493166+.2075033380*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, S[1] = 1/2*3^(1/2)+1/2*I, S[2] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4325617835-.4216939044*I+(.1404557731-.4337646272*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, S[1] = 1/2*3^(1/2)+1/2*I, S[2] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E9 11.10.E9] || [[Item:Q4026|<math>\WeberE{\nu}@{z} = \sin@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)-\cos@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{\nu}@{z} = \sin@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)-\cos@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE(nu, z) = sin((1)/(2)*Pi*nu)*S[1](nu , z)- cos((1)/(2)*Pi*nu)*S[2](nu , z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[\[Nu], z] == Sin[Divide[1,2]*Pi*\[Nu]]*Subscript[S, 1][\[Nu], z]- Cos[Divide[1,2]*Pi*\[Nu]]*Subscript[S, 2][\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6530158617-.8867638354e-1*I-(.3667170623+1.402184312*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, S[1] = 1/2*3^(1/2)+1/2*I, S[2] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .6530158617-.8867638354e-1*I-(.4337646272+.1404557731*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, S[1] = 1/2*3^(1/2)+1/2*I, S[2] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E10 11.10.E10] || [[Item:Q4027|<math>S_{1}(\nu,z) = \sum_{k=0}^{\infty}\frac{(-1)^{k}(\tfrac{1}{2}z)^{2k}}{\EulerGamma@{k\!+\!\tfrac{1}{2}\nu+1}\EulerGamma@{k\!-\!\tfrac{1}{2}\nu\!+\!1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>S_{1}(\nu,z) = \sum_{k=0}^{\infty}\frac{(-1)^{k}(\tfrac{1}{2}z)^{2k}}{\EulerGamma@{k\!+\!\tfrac{1}{2}\nu+1}\EulerGamma@{k\!-\!\tfrac{1}{2}\nu\!+\!1}}</syntaxhighlight> || <math>\realpart@@{k+\tfrac{1}{2}\nu+1} > 0, \realpart@@{k-\tfrac{1}{2}\nu+1} > 0</math> || <syntaxhighlight lang=mathematica>S[1](nu , z) = sum(((- 1)^(k)*((1)/(2)*z)^(2*k))/(GAMMA(k +(1)/(2)*nu + 1)*GAMMA(k -(1)/(2)*nu + 1)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[S, 1][\[Nu], z] == Sum[Divide[(- 1)^(k)*(Divide[1,2]*z)^(2*k),Gamma[k +Divide[1,2]*\[Nu]+ 1]*Gamma[k -Divide[1,2]*\[Nu]+ 1]], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: (.8660254040+.5000000000*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)-.6234597010+.4805214665*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, S[1] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: (-.5000000000+.8660254040*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)-.6234597010+.4805214665*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, S[1] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E11 11.10.E11] || [[Item:Q4028|<math>S_{2}(\nu,z) = \sum_{k=0}^{\infty}\frac{(-1)^{k}(\tfrac{1}{2}z)^{2k+1}}{\EulerGamma@{k\!+\!\tfrac{1}{2}\nu\!+\!\tfrac{3}{2}}\EulerGamma@{k\!-\!\tfrac{1}{2}\nu\!+\!\tfrac{3}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>S_{2}(\nu,z) = \sum_{k=0}^{\infty}\frac{(-1)^{k}(\tfrac{1}{2}z)^{2k+1}}{\EulerGamma@{k\!+\!\tfrac{1}{2}\nu\!+\!\tfrac{3}{2}}\EulerGamma@{k\!-\!\tfrac{1}{2}\nu\!+\!\tfrac{3}{2}}}</syntaxhighlight> || <math>\realpart@@{k+\tfrac{1}{2}\nu+\tfrac{3}{2}} > 0, \realpart@@{k-\tfrac{1}{2}\nu+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>S[2](nu , z) = sum(((- 1)^(k)*((1)/(2)*z)^(2*k + 1))/(GAMMA(k +(1)/(2)*nu +(3)/(2))*GAMMA(k -(1)/(2)*nu +(3)/(2))), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[S, 2][\[Nu], z] == Sum[Divide[(- 1)^(k)*(Divide[1,2]*z)^(2*k + 1),Gamma[k +Divide[1,2]*\[Nu]+Divide[3,2]]*Gamma[k -Divide[1,2]*\[Nu]+Divide[3,2]]], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: (.8660254040+.5000000000*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)-.4892722811e-1+.1117224133*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, S[2] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: (-.5000000000+.8660254040*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)-.4892722811e-1+.1117224133*I
| |
| Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, S[2] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10#Ex1 11.10#Ex1] || [[Item:Q4029|<math>\AngerJ{\nu}@{-z} = \AngerJ{-\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\nu}@{-z} = \AngerJ{-\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(nu, - z) = AngerJ(- nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[\[Nu], - z] == AngerJ[- \[Nu], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10#Ex2 11.10#Ex2] || [[Item:Q4030|<math>\WeberE{\nu}@{-z} = -\WeberE{-\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{\nu}@{-z} = -\WeberE{-\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE(nu, - z) = - WeberE(- nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[\[Nu], - z] == - WeberE[- \[Nu], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E13 11.10.E13] || [[Item:Q4031|<math>\sin@{\pi\nu}\,\AngerJ{\nu}@{z} = \cos@{\pi\nu}\,\WeberE{\nu}@{z}-\WeberE{-\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@{\pi\nu}\,\AngerJ{\nu}@{z} = \cos@{\pi\nu}\,\WeberE{\nu}@{z}-\WeberE{-\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sin(Pi*nu)*AngerJ(nu, z) = cos(Pi*nu)*WeberE(nu, z)- WeberE(- nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[Pi*\[Nu]]*AngerJ[\[Nu], z] == Cos[Pi*\[Nu]]*WeberE[\[Nu], z]- WeberE[- \[Nu], z]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E14 11.10.E14] || [[Item:Q4032|<math>\sin@{\pi\nu}\,\WeberE{\nu}@{z} = \AngerJ{-\nu}@{z}-\cos@{\pi\nu}\,\AngerJ{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@{\pi\nu}\,\WeberE{\nu}@{z} = \AngerJ{-\nu}@{z}-\cos@{\pi\nu}\,\AngerJ{\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sin(Pi*nu)*WeberE(nu, z) = AngerJ(- nu, z)- cos(Pi*nu)*AngerJ(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[Pi*\[Nu]]*WeberE[\[Nu], z] == AngerJ[- \[Nu], z]- Cos[Pi*\[Nu]]*AngerJ[\[Nu], z]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E17 11.10.E17] || [[Item:Q4035|<math>\AngerJ{\nu}@{z} = \frac{\sin@{\pi\nu}}{\pi}(\Lommels{0}{\nu}@{z}-\nu\Lommels{-1}{\nu}@{z})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\nu}@{z} = \frac{\sin@{\pi\nu}}{\pi}(\Lommels{0}{\nu}@{z}-\nu\Lommels{-1}{\nu}@{z})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(nu, z) = (sin(Pi*nu))/(Pi)*(LommelS1(0, nu, z)- nu*LommelS1(- 1, nu, z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E18 11.10.E18] || [[Item:Q4036|<math>\WeberE{\nu}@{z} = -\frac{1}{\pi}(1+\cos@{\pi\nu})\Lommels{0}{\nu}@{z}\\ -\frac{\nu}{\pi}(1-\cos@{\pi\nu})\Lommels{-1}{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{\nu}@{z} = -\frac{1}{\pi}(1+\cos@{\pi\nu})\Lommels{0}{\nu}@{z}\\ -\frac{\nu}{\pi}(1-\cos@{\pi\nu})\Lommels{-1}{\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE(nu, z) = -(1)/(Pi)*(1 + cos(Pi*nu))*LommelS1(0, nu, z)*; -(nu)/(Pi)*(1 - cos(Pi*nu))* LommelS1(- 1, nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E19 11.10.E19] || [[Item:Q4037|<math>\AngerJ{-\frac{1}{2}}@{z} = \WeberE{\frac{1}{2}}@{z}\\</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{-\frac{1}{2}}@{z} = \WeberE{\frac{1}{2}}@{z}\\</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(-(1)/(2), z) = WeberE((1)/(2), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[-Divide[1,2], z] == WeberE[Divide[1,2], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E19 11.10.E19] || [[Item:Q4037|<math>\WeberE{\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\cos@@{z}-A_{-}(\chi)\sin@@{z})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\cos@@{z}-A_{-}(\chi)\sin@@{z})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE((1)/(2), z) = ((1)/(2)*Pi*z)^(-(1)/(2))*(A[+](chi)* cos(z)- A[-](chi)* sin(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[Divide[1,2], z] == (Divide[1,2]*Pi*z)^(-Divide[1,2])*(Subscript[A, +][\[Chi]]* Cos[z]- Subscript[A, -][\[Chi]]* Sin[z])</syntaxhighlight> || Error || Failure || - || Error
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E20 11.10.E20] || [[Item:Q4038|<math>\AngerJ{\frac{1}{2}}@{z} = -\WeberE{-\frac{1}{2}}@{z}\\</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\frac{1}{2}}@{z} = -\WeberE{-\frac{1}{2}}@{z}\\</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ((1)/(2), z) = - WeberE(-(1)/(2), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[Divide[1,2], z] == - WeberE[-Divide[1,2], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E20 11.10.E20] || [[Item:Q4038|<math>-\WeberE{-\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\sin@@{z}+A_{-}(\chi)\cos@@{z})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\WeberE{-\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\sin@@{z}+A_{-}(\chi)\cos@@{z})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- WeberE(-(1)/(2), z) = ((1)/(2)*Pi*z)^(-(1)/(2))*(A[+](chi)* sin(z)+ A[-](chi)* cos(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>- WeberE[-Divide[1,2], z] == (Divide[1,2]*Pi*z)^(-Divide[1,2])*(Subscript[A, +][\[Chi]]* Sin[z]+ Subscript[A, -][\[Chi]]* Cos[z])</syntaxhighlight> || Error || Failure || - || Error
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10#Ex3 11.10#Ex3] || [[Item:Q4039|<math>A_{+}(\chi) = \Fresnelcosint@{\chi}+\Fresnelsinint@{\chi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>A_{+}(\chi) = \Fresnelcosint@{\chi}+\Fresnelsinint@{\chi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>A[+](chi) = FresnelC(chi)+ FresnelS(chi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[A, +][\[Chi]] == FresnelC[\[Chi]]+ FresnelS[\[Chi]]</syntaxhighlight> || Error || Failure || - || Error
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10#Ex3 11.10#Ex3] || [[Item:Q4039|<math>A_{-}(\chi) = \Fresnelcosint@{\chi}-\Fresnelsinint@{\chi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>A_{-}(\chi) = \Fresnelcosint@{\chi}-\Fresnelsinint@{\chi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>A[-](chi) = FresnelC(chi)- FresnelS(chi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[A, -][\[Chi]] == FresnelC[\[Chi]]- FresnelS[\[Chi]]</syntaxhighlight> || Error || Failure || - || Error
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10#Ex4 11.10#Ex4] || [[Item:Q4040|<math>\chi = (2z/\pi)^{\frac{1}{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\chi = (2z/\pi)^{\frac{1}{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>chi = (2*z/Pi)^((1)/(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Chi] == (2*z/Pi)^(Divide[1,2])</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E22 11.10.E22] || [[Item:Q4041|<math>\WeberE{n}@{z} = -\StruveH{n}@{z}+\frac{1}{\pi}\sum_{k=0}^{m_{1}}\frac{\EulerGamma@{k+\tfrac{1}{2}}}{\EulerGamma@{n\!+\!\tfrac{1}{2}\!-\!k}}(\tfrac{1}{2}z)^{n-2k-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{n}@{z} = -\StruveH{n}@{z}+\frac{1}{\pi}\sum_{k=0}^{m_{1}}\frac{\EulerGamma@{k+\tfrac{1}{2}}}{\EulerGamma@{n\!+\!\tfrac{1}{2}\!-\!k}}(\tfrac{1}{2}z)^{n-2k-1}</syntaxhighlight> || <math>\realpart@@{k+\tfrac{1}{2}} > 0, \realpart@@{n+\tfrac{1}{2}-k} > 0, \realpart@@{n+n+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>WeberE(n, z) = - StruveH(n, z)+(1)/(Pi)*sum((GAMMA(k +(1)/(2)))/(GAMMA(n +(1)/(2)- k))*((1)/(2)*z)^(n - 2*k - 1), k = 0..m[1])</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[n, z] == - StruveH[n, z]+Divide[1,Pi]*Sum[Divide[Gamma[k +Divide[1,2]],Gamma[n +Divide[1,2]- k]]*(Divide[1,2]*z)^(n - 2*k - 1), {k, 0, Subscript[m, 1]}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Manual Skip! || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[0.6366197723675814, Times[-0.3183098861837907, DifferenceRoot[Function[{, }
| |
| Test Values: {Equal[Plus[Times[-1, Plus[-1, Times[2, ]], Plus[1, Times[2, ]], []], Times[Plus[-1, Times[-1, Power[-1, Rational[1, 3]]], Times[4, Power[, 2]]], [Plus[1, ]]], Times[Power[-1, Rational[1, 3]], [Plus[2, ]]]], 0], Equal[[0], 0], Equal[[1], 2]}]][Complex[1.8660254037844388, 0.49999999999999994]]]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[m, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.18377629847393068, 0.10610329539459687], Times[Complex[-0.13783222385544802, -0.07957747154594766], DifferenceRoot[Function[{, }
| |
| Test Values: {Equal[Plus[Times[-1, Plus[-3, Times[2, ]], Plus[1, Times[2, ]], []], Times[Plus[-3, Times[-1, Power[-1, Rational[1, 3]]], Times[-4, ], Times[4, Power[, 2]]], [Plus[1, ]]], Times[Po</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E23 11.10.E23] || [[Item:Q4042|<math>\WeberE{-n}@{z} = -\StruveH{-n}@{z}+\frac{(-1)^{n+1}}{\pi}\sum_{k=0}^{m_{2}}\frac{\EulerGamma@{n\!-\!k\!-\!\tfrac{1}{2}}}{\EulerGamma@{k+\tfrac{3}{2}}}(\tfrac{1}{2}z)^{-n+2k+1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{-n}@{z} = -\StruveH{-n}@{z}+\frac{(-1)^{n+1}}{\pi}\sum_{k=0}^{m_{2}}\frac{\EulerGamma@{n\!-\!k\!-\!\tfrac{1}{2}}}{\EulerGamma@{k+\tfrac{3}{2}}}(\tfrac{1}{2}z)^{-n+2k+1}</syntaxhighlight> || <math>\realpart@@{n-k-\tfrac{1}{2}} > 0, \realpart@@{k+\tfrac{3}{2}} > 0, \realpart@@{n+-n+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>WeberE(- n, z) = - StruveH(- n, z)+((- 1)^(n + 1))/(Pi)*sum((GAMMA(n - k -(1)/(2)))/(GAMMA(k +(3)/(2)))*((1)/(2)*z)^(- n + 2*k + 1), k = 0..m[2])</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[- n, z] == - StruveH[- n, z]+Divide[(- 1)^(n + 1),Pi]*Sum[Divide[Gamma[n - k -Divide[1,2]],Gamma[k +Divide[3,2]]]*(Divide[1,2]*z)^(- n + 2*k + 1), {k, 0, Subscript[m, 2]}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.5182370935+.1715162156*I
| |
| Test Values: {z = 1/2*3^(1/2)+1/2*I, m[2] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1977910573+.6179671328e-1*I
| |
| Test Values: {z = 1/2*3^(1/2)+1/2*I, m[2] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.5182370936641069, 0.17151621559870867]
| |
| Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[m, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.19779105745155356, 0.06179671324201291]
| |
| Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[m, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10#Ex5 11.10#Ex5] || [[Item:Q4043|<math>m_{1} = \floor{\tfrac{1}{2}n-\tfrac{1}{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>m_{1} = \floor{\tfrac{1}{2}n-\tfrac{1}{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>m[1] = floor((1)/(2)*n -(1)/(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[m, 1] == Floor[Divide[1,2]*n -Divide[1,2]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
| |
| Test Values: {m[1] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
| |
| Test Values: {m[1] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.8660254037844387, 0.49999999999999994]
| |
| Test Values: {Rule[n, 1], Rule[Subscript[m, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.8660254037844387, 0.49999999999999994]
| |
| Test Values: {Rule[n, 2], Rule[Subscript[m, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10#Ex6 11.10#Ex6] || [[Item:Q4044|<math>m_{2} = \ceiling{\tfrac{1}{2}n-\tfrac{3}{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>m_{2} = \ceiling{\tfrac{1}{2}n-\tfrac{3}{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>m[2] = ceil((1)/(2)*n -(3)/(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[m, 2] == Ceiling[Divide[1,2]*n -Divide[3,2]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.866025404+.5000000000*I
| |
| Test Values: {m[2] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
| |
| Test Values: {m[2] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.8660254037844388, 0.49999999999999994]
| |
| Test Values: {Rule[n, 1], Rule[Subscript[m, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.8660254037844387, 0.49999999999999994]
| |
| Test Values: {Rule[n, 2], Rule[Subscript[m, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E25 11.10.E25] || [[Item:Q4046|<math>\displaystyle\AngerJ{\nu}@{0} = \frac{\sin@{\pi\nu}}{\pi\nu}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\displaystyle\AngerJ{\nu}@{0} = \frac{\sin@{\pi\nu}}{\pi\nu}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(nu, 0) = (sin(Pi*nu))/(Pi*nu)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[\[Nu], 0] == Divide[Sin[Pi*\[Nu]],Pi*\[Nu]]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E25 11.10.E25] || [[Item:Q4046|<math>\displaystyle\WeberE{\nu}@{0} = \frac{1-\cos@{\pi\nu}}{\pi\nu}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\displaystyle\WeberE{\nu}@{0} = \frac{1-\cos@{\pi\nu}}{\pi\nu}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE(nu, 0) = (1 - cos(Pi*nu))/(Pi*nu)</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[\[Nu], 0] == Divide[1 - Cos[Pi*\[Nu]],Pi*\[Nu]]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E26 11.10.E26] || [[Item:Q4048|<math>\displaystyle\WeberE{0}@{z} = -\StruveH{0}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\displaystyle\WeberE{0}@{z} = -\StruveH{0}@{z}</syntaxhighlight> || <math>\realpart@@{n+0+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>WeberE(0, z) = - StruveH(0, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[0, z] == - StruveH[0, z]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E26 11.10.E26] || [[Item:Q4048|<math>\displaystyle\WeberE{1}@{z} = \frac{2}{\pi}-\StruveH{1}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\displaystyle\WeberE{1}@{z} = \frac{2}{\pi}-\StruveH{1}@{z}</syntaxhighlight> || <math>\realpart@@{n+1+\tfrac{3}{2}} > 0</math> || <syntaxhighlight lang=mathematica>WeberE(1, z) = (2)/(Pi)- StruveH(1, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[1, z] == Divide[2,Pi]- StruveH[1, z]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E29 11.10.E29] || [[Item:Q4051|<math>\AngerJ{n}@{z} = \BesselJ{n}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{n}@{z} = \BesselJ{n}@{z}</syntaxhighlight> || <math>\realpart@@{n+k+1} > 0</math> || <syntaxhighlight lang=mathematica>AngerJ(n, z) = BesselJ(n, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[n, z] == BesselJ[n, z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E32 11.10.E32] || [[Item:Q4054|<math>\AngerJ{\nu-1}@{z}+\AngerJ{\nu+1}@{z} = \frac{2\nu}{z}\AngerJ{\nu}@{z}-\frac{2}{\pi z}\sin@{\pi\nu}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\nu-1}@{z}+\AngerJ{\nu+1}@{z} = \frac{2\nu}{z}\AngerJ{\nu}@{z}-\frac{2}{\pi z}\sin@{\pi\nu}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(nu - 1, z)+ AngerJ(nu + 1, z) = (2*nu)/(z)*AngerJ(nu, z)-(2)/(Pi*z)*sin(Pi*nu)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[\[Nu]- 1, z]+ AngerJ[\[Nu]+ 1, z] == Divide[2*\[Nu],z]*AngerJ[\[Nu], z]-Divide[2,Pi*z]*Sin[Pi*\[Nu]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1812319651
| |
| Test Values: {nu = -3/2, z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1208213102
| |
| Test Values: {nu = -1/2, z = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E33 11.10.E33] || [[Item:Q4055|<math>\WeberE{\nu-1}@{z}+\WeberE{\nu+1}@{z} = \frac{2\nu}{z}\WeberE{\nu}@{z}-\frac{2}{\pi z}(1-\cos@{\pi\nu})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{\nu-1}@{z}+\WeberE{\nu+1}@{z} = \frac{2\nu}{z}\WeberE{\nu}@{z}-\frac{2}{\pi z}(1-\cos@{\pi\nu})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE(nu - 1, z)+ WeberE(nu + 1, z) = (2*nu)/(z)*WeberE(nu, z)-(2)/(Pi*z)*(1 - cos(Pi*nu))</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[\[Nu]- 1, z]+ WeberE[\[Nu]+ 1, z] == Divide[2*\[Nu],z]*WeberE[\[Nu], z]-Divide[2,Pi*z]*(1 - Cos[Pi*\[Nu]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1812319648
| |
| Test Values: {nu = 3/2, z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1812319652
| |
| Test Values: {nu = -1/2, z = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E34 11.10.E34] || [[Item:Q4056|<math>2\AngerJ{\nu}'@{z} = \AngerJ{\nu-1}@{z}-\AngerJ{\nu+1}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2\AngerJ{\nu}'@{z} = \AngerJ{\nu-1}@{z}-\AngerJ{\nu+1}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>2*diff( AngerJ(nu, z), z$(1) ) = AngerJ(nu - 1, z)- AngerJ(nu + 1, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*D[AngerJ[\[Nu], z], {z, 1}] == AngerJ[\[Nu]- 1, z]- AngerJ[\[Nu]+ 1, z]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1812319651
| |
| Test Values: {nu = -3/2, z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1208213102
| |
| Test Values: {nu = -1/2, z = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E35 11.10.E35] || [[Item:Q4057|<math>2\WeberE{\nu}'@{z} = \WeberE{\nu-1}@{z}-\WeberE{\nu+1}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2\WeberE{\nu}'@{z} = \WeberE{\nu-1}@{z}-\WeberE{\nu+1}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>2*diff( WeberE(nu, z), z$(1) ) = WeberE(nu - 1, z)- WeberE(nu + 1, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*D[WeberE[\[Nu], z], {z, 1}] == WeberE[\[Nu]- 1, z]- WeberE[\[Nu]+ 1, z]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1812319648
| |
| Test Values: {nu = 3/2, z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1812319652
| |
| Test Values: {nu = -1/2, z = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E36 11.10.E36] || [[Item:Q4058|<math>z\AngerJ{\nu}'@{z}+\nu\AngerJ{\nu}@{z} = + z\AngerJ{\nu- 1}@{z}+\frac{\sin@{\pi\nu}}{\pi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\AngerJ{\nu}'@{z}+\nu\AngerJ{\nu}@{z} = + z\AngerJ{\nu- 1}@{z}+\frac{\sin@{\pi\nu}}{\pi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*diff( AngerJ(nu, z), z$(1) )+ nu*AngerJ(nu, z) = + z*AngerJ(nu - 1, z)+(sin(Pi*nu))/(Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*D[AngerJ[\[Nu], z], {z, 1}]+ \[Nu]*AngerJ[\[Nu], z] == + z*AngerJ[\[Nu]- 1, z]+Divide[Sin[Pi*\[Nu]],Pi]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2718479477
| |
| Test Values: {nu = -3/2, z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1812319655
| |
| Test Values: {nu = -1/2, z = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E36 11.10.E36] || [[Item:Q4058|<math>z\AngerJ{\nu}'@{z}-\nu\AngerJ{\nu}@{z} = - z\AngerJ{\nu+ 1}@{z}-\frac{\sin@{\pi\nu}}{\pi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\AngerJ{\nu}'@{z}-\nu\AngerJ{\nu}@{z} = - z\AngerJ{\nu+ 1}@{z}-\frac{\sin@{\pi\nu}}{\pi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*diff( AngerJ(nu, z), z$(1) )- nu*AngerJ(nu, z) = - z*AngerJ(nu + 1, z)-(sin(Pi*nu))/(Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*D[AngerJ[\[Nu], z], {z, 1}]- \[Nu]*AngerJ[\[Nu], z] == - z*AngerJ[\[Nu]+ 1, z]-Divide[Sin[Pi*\[Nu]],Pi]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E37 11.10.E37] || [[Item:Q4059|<math>z\WeberE{\nu}'@{z}+\nu\WeberE{\nu}@{z} = + z\WeberE{\nu- 1}@{z}+\frac{(1-\cos@{\pi\nu})}{\pi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\WeberE{\nu}'@{z}+\nu\WeberE{\nu}@{z} = + z\WeberE{\nu- 1}@{z}+\frac{(1-\cos@{\pi\nu})}{\pi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*diff( WeberE(nu, z), z$(1) )+ nu*WeberE(nu, z) = + z*WeberE(nu - 1, z)+(1 - cos(Pi*nu))/(Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*D[WeberE[\[Nu], z], {z, 1}]+ \[Nu]*WeberE[\[Nu], z] == + z*WeberE[\[Nu]- 1, z]+Divide[1 - Cos[Pi*\[Nu]],Pi]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2718479477
| |
| Test Values: {nu = 3/2, z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2718479472
| |
| Test Values: {nu = -1/2, z = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.10.E37 11.10.E37] || [[Item:Q4059|<math>z\WeberE{\nu}'@{z}-\nu\WeberE{\nu}@{z} = - z\WeberE{\nu+ 1}@{z}-\frac{(1-\cos@{\pi\nu})}{\pi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\WeberE{\nu}'@{z}-\nu\WeberE{\nu}@{z} = - z\WeberE{\nu+ 1}@{z}-\frac{(1-\cos@{\pi\nu})}{\pi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*diff( WeberE(nu, z), z$(1) )- nu*WeberE(nu, z) = - z*WeberE(nu + 1, z)-(1 - cos(Pi*nu))/(Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*D[WeberE[\[Nu], z], {z, 1}]- \[Nu]*WeberE[\[Nu], z] == - z*WeberE[\[Nu]+ 1, z]-Divide[1 - Cos[Pi*\[Nu]],Pi]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 70]
| |
| |-
| |
| | [https://dlmf.nist.gov/11.11#Ex1 11.11#Ex1] || [[Item:Q4070|<math>a_{0}(\lambda) = \frac{1}{1+\lambda}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>a_{0}(\lambda) = \frac{1}{1+\lambda}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>a[0](lambda) = (1)/(1 + lambda)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[a, 0][\[Lambda]] == Divide[1,1 + \[Lambda]]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.11#Ex2 11.11#Ex2] || [[Item:Q4071|<math>a_{1}(\lambda) = -\frac{\lambda}{2(1+\lambda)^{4}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>a_{1}(\lambda) = -\frac{\lambda}{2(1+\lambda)^{4}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>a[1](lambda) = -(lambda)/(2*(1 + lambda)^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[a, 1][\[Lambda]] == -Divide[\[Lambda],2*(1 + \[Lambda])^(4)]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.11#Ex3 11.11#Ex3] || [[Item:Q4072|<math>a_{2}(\lambda) = \frac{9\lambda^{2}-\lambda}{24(1+\lambda)^{7}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>a_{2}(\lambda) = \frac{9\lambda^{2}-\lambda}{24(1+\lambda)^{7}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>a[2](lambda) = (9*(lambda)^(2)- lambda)/(24*(1 + lambda)^(7))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[a, 2][\[Lambda]] == Divide[9*\[Lambda]^(2)- \[Lambda],24*(1 + \[Lambda])^(7)]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.11#Ex4 11.11#Ex4] || [[Item:Q4073|<math>a_{3}(\lambda) = -\frac{225\lambda^{3}-54\lambda^{2}+\lambda}{720(1+\lambda)^{10}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>a_{3}(\lambda) = -\frac{225\lambda^{3}-54\lambda^{2}+\lambda}{720(1+\lambda)^{10}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>a[3](lambda) = -(225*(lambda)^(3)- 54*(lambda)^(2)+ lambda)/(720*(1 + lambda)^(10))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[a, 3][\[Lambda]] == -Divide[225*\[Lambda]^(3)- 54*\[Lambda]^(2)+ \[Lambda],720*(1 + \[Lambda])^(10)]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.11.E12 11.11.E12] || [[Item:Q4076|<math>\mu = \sqrt{1-\lambda^{2}}-\ln@{\frac{1+\sqrt{1-\lambda^{2}}}{\lambda}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\mu = \sqrt{1-\lambda^{2}}-\ln@{\frac{1+\sqrt{1-\lambda^{2}}}{\lambda}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>mu = sqrt(1 - (lambda)^(2))- ln((1 +sqrt(1 - (lambda)^(2)))/(lambda))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Mu] == Sqrt[1 - \[Lambda]^(2)]- Log[Divide[1 +Sqrt[1 - \[Lambda]^(2)],\[Lambda]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [100 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6584789489+.2146018366*I
| |
| Test Values: {lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.7075464554+.5806272406*I
| |
| Test Values: {lambda = 1/2*3^(1/2)+1/2*I, mu = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [100 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.6584789484624085, 0.21460183660255172]
| |
| Test Values: {Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.70754645532203, 0.5806272403869905]
| |
| Test Values: {Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/11.11#Ex5 11.11#Ex5] || [[Item:Q4077|<math>b_{0}(\lambda) = \frac{1}{(1-\lambda^{2})^{1/4}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>b_{0}(\lambda) = \frac{1}{(1-\lambda^{2})^{1/4}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>b[0](lambda) = (1)/((1 - (lambda)^(2))^(1/4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[b, 0][\[Lambda]] == Divide[1,(1 - \[Lambda]^(2))^(1/4)]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.11#Ex6 11.11#Ex6] || [[Item:Q4078|<math>b_{1}(\lambda) = \frac{2+3\lambda^{2}}{12(1-\lambda^{2})^{7/4}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>b_{1}(\lambda) = \frac{2+3\lambda^{2}}{12(1-\lambda^{2})^{7/4}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>b[1](lambda) = (2 + 3*(lambda)^(2))/(12*(1 - (lambda)^(2))^(7/4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[b, 1][\[Lambda]] == Divide[2 + 3*\[Lambda]^(2),12*(1 - \[Lambda]^(2))^(7/4)]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/11.11#Ex7 11.11#Ex7] || [[Item:Q4079|<math>b_{2}(\lambda) = \frac{4+300\lambda^{2}+81\lambda^{4}}{864(1-\lambda^{2})^{13/4}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>b_{2}(\lambda) = \frac{4+300\lambda^{2}+81\lambda^{4}}{864(1-\lambda^{2})^{13/4}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>b[2](lambda) = (4 + 300*(lambda)^(2)+ 81*(lambda)^(4))/(864*(1 - (lambda)^(2))^(13/4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[b, 2][\[Lambda]] == Divide[4 + 300*\[Lambda]^(2)+ 81*\[Lambda]^(4),864*(1 - \[Lambda]^(2))^(13/4)]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| |}
| |