19.22: Difference between revisions

From testwiki
Jump to navigation Jump to search
 
 
Line 14: Line 14:
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
|-  
|-  
| [https://dlmf.nist.gov/19.22.E1 19.22.E1] || [[Item:Q6436|<math>\CarlsonsymellintRF@{0}{x^{2}}{y^{2}} = \CarlsonsymellintRF@{0}{xy}{a^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRF@{0}{x^{2}}{y^{2}} = \CarlsonsymellintRF@{0}{xy}{a^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>0.5*int(1/(sqrt(t+0)*sqrt(t+(x)^(2))*sqrt(t+(y)^(2))), t = 0..infinity) = 0.5*int(1/(sqrt(t+0)*sqrt(t+x*y)*sqrt(t+(a)^(2))), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]/Sqrt[(y)^(2)-0] == EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]</syntaxhighlight> || Aborted || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [102 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.1731783664325578, 0.8740191847640398]
| [https://dlmf.nist.gov/19.22.E1 19.22.E1] || <math qid="Q6436">\CarlsonsymellintRF@{0}{x^{2}}{y^{2}} = \CarlsonsymellintRF@{0}{xy}{a^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRF@{0}{x^{2}}{y^{2}} = \CarlsonsymellintRF@{0}{xy}{a^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>0.5*int(1/(sqrt(t+0)*sqrt(t+(x)^(2))*sqrt(t+(y)^(2))), t = 0..infinity) = 0.5*int(1/(sqrt(t+0)*sqrt(t+x*y)*sqrt(t+(a)^(2))), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]/Sqrt[(y)^(2)-0] == EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]</syntaxhighlight> || Aborted || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [102 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.1731783664325578, 0.8740191847640398]
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.4406854652170371, 0.9732684211375591]
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.4406854652170371, 0.9732684211375591]
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-  
|-  
| [https://dlmf.nist.gov/19.22.E2 19.22.E2] || [[Item:Q6437|<math>2\CarlsonsymellintRG@{0}{x^{2}}{y^{2}} = 4\CarlsonsymellintRG@{0}{xy}{a^{2}}-xy\CarlsonsymellintRF@{0}{xy}{a^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2\CarlsonsymellintRG@{0}{x^{2}}{y^{2}} = 4\CarlsonsymellintRG@{0}{xy}{a^{2}}-xy\CarlsonsymellintRF@{0}{xy}{a^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*Sqrt[(y)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(y)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]+Cot[ArcCos[Sqrt[0/(y)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(y)^(2)]]]^2]) == 4*Sqrt[(a)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(a)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]+Cot[ArcCos[Sqrt[0/(a)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(a)^(2)]]]^2])- x*y*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [108 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.848574889541176, -1.6278775384876862]
| [https://dlmf.nist.gov/19.22.E2 19.22.E2] || <math qid="Q6437">2\CarlsonsymellintRG@{0}{x^{2}}{y^{2}} = 4\CarlsonsymellintRG@{0}{xy}{a^{2}}-xy\CarlsonsymellintRF@{0}{xy}{a^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2\CarlsonsymellintRG@{0}{x^{2}}{y^{2}} = 4\CarlsonsymellintRG@{0}{xy}{a^{2}}-xy\CarlsonsymellintRF@{0}{xy}{a^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*Sqrt[(y)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(y)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]+Cot[ArcCos[Sqrt[0/(y)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(y)^(2)]]]^2]) == 4*Sqrt[(a)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(a)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]+Cot[ArcCos[Sqrt[0/(a)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(a)^(2)]]]^2])- x*y*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [108 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.848574889541176, -1.6278775384876862]
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.356194490192345
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.356194490192345
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-  
|-  
| [https://dlmf.nist.gov/19.22.E3 19.22.E3] || [[Item:Q6438|<math>2y^{2}\CarlsonsymellintRD@{0}{x^{2}}{y^{2}} = \tfrac{1}{4}(y^{2}-x^{2})\CarlsonsymellintRD@{0}{xy}{a^{2}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2y^{2}\CarlsonsymellintRD@{0}{x^{2}}{y^{2}} = \tfrac{1}{4}(y^{2}-x^{2})\CarlsonsymellintRD@{0}{xy}{a^{2}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*(y)^(2)* 3*(EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/(((y)^(2)-(x)^(2))*((y)^(2)-0)^(1/2)) == Divide[1,4]*((y)^(2)- (x)^(2))*3*(EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/(((a)^(2)-x*y)*((a)^(2)-0)^(1/2))+ 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [108 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
| [https://dlmf.nist.gov/19.22.E3 19.22.E3] || <math qid="Q6438">2y^{2}\CarlsonsymellintRD@{0}{x^{2}}{y^{2}} = \tfrac{1}{4}(y^{2}-x^{2})\CarlsonsymellintRD@{0}{xy}{a^{2}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2y^{2}\CarlsonsymellintRD@{0}{x^{2}}{y^{2}} = \tfrac{1}{4}(y^{2}-x^{2})\CarlsonsymellintRD@{0}{xy}{a^{2}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*(y)^(2)* 3*(EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/(((y)^(2)-(x)^(2))*((y)^(2)-0)^(1/2)) == Divide[1,4]*((y)^(2)- (x)^(2))*3*(EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/(((a)^(2)-x*y)*((a)^(2)-0)^(1/2))+ 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [108 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-  
|-  
| [https://dlmf.nist.gov/19.22.E4 19.22.E4] || [[Item:Q6439|<math>(p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>((Subscript[p, +])^(2)- (Subscript[p, -])^(2))*3*((y)^(2)-0)/((y)^(2)-(p)^(2))*(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == 2*((Subscript[p, +])^(2)- (a)^(2))*3*((a)^(2)-0)/((a)^(2)-(Subscript[p, +])^(2))*(EllipticPi[((a)^(2)-(Subscript[p, +])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]- 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]+ 3*Pi/(2*p)</syntaxhighlight> || Missing Macro Error || Failure || - || Error
| [https://dlmf.nist.gov/19.22.E4 19.22.E4] || <math qid="Q6439">(p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>((Subscript[p, +])^(2)- (Subscript[p, -])^(2))*3*((y)^(2)-0)/((y)^(2)-(p)^(2))*(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == 2*((Subscript[p, +])^(2)- (a)^(2))*3*((a)^(2)-0)/((a)^(2)-(Subscript[p, +])^(2))*(EllipticPi[((a)^(2)-(Subscript[p, +])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]- 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]+ 3*Pi/(2*p)</syntaxhighlight> || Missing Macro Error || Failure || - || Error
|-  
|-  
| [https://dlmf.nist.gov/19.22.E4 19.22.E4] || [[Item:Q6439|<math>(p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>((Subscript[p, -])^(2)- (Subscript[p, +])^(2))*3*((y)^(2)-0)/((y)^(2)-(p)^(2))*(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == 2*((Subscript[p, -])^(2)- (a)^(2))*3*((a)^(2)-0)/((a)^(2)-(Subscript[p, -])^(2))*(EllipticPi[((a)^(2)-(Subscript[p, -])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]- 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]+ 3*Pi/(2*p)</syntaxhighlight> || Missing Macro Error || Failure || - || Error
| [https://dlmf.nist.gov/19.22.E4 19.22.E4] || <math qid="Q6439">(p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>((Subscript[p, -])^(2)- (Subscript[p, +])^(2))*3*((y)^(2)-0)/((y)^(2)-(p)^(2))*(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == 2*((Subscript[p, -])^(2)- (a)^(2))*3*((a)^(2)-0)/((a)^(2)-(Subscript[p, -])^(2))*(EllipticPi[((a)^(2)-(Subscript[p, -])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]- 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]+ 3*Pi/(2*p)</syntaxhighlight> || Missing Macro Error || Failure || - || Error
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex1 19.22#Ex1] || [[Item:Q6441|<math>p_{+}p_{-} = pa</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{+}p_{-} = pa</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">p[+]*p[-] = p*a</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[p, +]*Subscript[p, -] == p*a</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex1 19.22#Ex1] || <math qid="Q6441">p_{+}p_{-} = pa</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{+}p_{-} = pa</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">p[+]*p[-] = p*a</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[p, +]*Subscript[p, -] == p*a</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex2 19.22#Ex2] || [[Item:Q6442|<math>p_{+}^{2}+p_{-}^{2} = p^{2}+xy</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{+}^{2}+p_{-}^{2} = p^{2}+xy</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(p[+])^(2)+ (p[-])^(2) = (p)^(2)+ x*y</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[p, +])^(2)+ (Subscript[p, -])^(2) == (p)^(2)+ x*y</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex2 19.22#Ex2] || <math qid="Q6442">p_{+}^{2}+p_{-}^{2} = p^{2}+xy</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{+}^{2}+p_{-}^{2} = p^{2}+xy</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(p[+])^(2)+ (p[-])^(2) = (p)^(2)+ x*y</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[p, +])^(2)+ (Subscript[p, -])^(2) == (p)^(2)+ x*y</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex3 19.22#Ex3] || [[Item:Q6443|<math>p_{+}^{2}-p_{-}^{2} = \sqrt{(p^{2}-x^{2})(p^{2}-y^{2})}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{+}^{2}-p_{-}^{2} = \sqrt{(p^{2}-x^{2})(p^{2}-y^{2})}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(p[+])^(2)- (p[-])^(2) = sqrt(((p)^(2)- (x)^(2))*((p)^(2)- (y)^(2)))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[p, +])^(2)- (Subscript[p, -])^(2) == Sqrt[((p)^(2)- (x)^(2))*((p)^(2)- (y)^(2))]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex3 19.22#Ex3] || <math qid="Q6443">p_{+}^{2}-p_{-}^{2} = \sqrt{(p^{2}-x^{2})(p^{2}-y^{2})}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{+}^{2}-p_{-}^{2} = \sqrt{(p^{2}-x^{2})(p^{2}-y^{2})}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(p[+])^(2)- (p[-])^(2) = sqrt(((p)^(2)- (x)^(2))*((p)^(2)- (y)^(2)))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[p, +])^(2)- (Subscript[p, -])^(2) == Sqrt[((p)^(2)- (x)^(2))*((p)^(2)- (y)^(2))]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex4 19.22#Ex4] || [[Item:Q6444|<math>4(p_{+}^{2}-a^{2}) = (\sqrt{p^{2}-x^{2}}+\sqrt{p^{2}-y^{2}})^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>4(p_{+}^{2}-a^{2}) = (\sqrt{p^{2}-x^{2}}+\sqrt{p^{2}-y^{2}})^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">4*((p[+])^(2)- (a)^(2)) = (sqrt((p)^(2)- (x)^(2))+sqrt((p)^(2)- (y)^(2)))^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">4*((Subscript[p, +])^(2)- (a)^(2)) == (Sqrt[(p)^(2)- (x)^(2)]+Sqrt[(p)^(2)- (y)^(2)])^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex4 19.22#Ex4] || <math qid="Q6444">4(p_{+}^{2}-a^{2}) = (\sqrt{p^{2}-x^{2}}+\sqrt{p^{2}-y^{2}})^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>4(p_{+}^{2}-a^{2}) = (\sqrt{p^{2}-x^{2}}+\sqrt{p^{2}-y^{2}})^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">4*((p[+])^(2)- (a)^(2)) = (sqrt((p)^(2)- (x)^(2))+sqrt((p)^(2)- (y)^(2)))^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">4*((Subscript[p, +])^(2)- (a)^(2)) == (Sqrt[(p)^(2)- (x)^(2)]+Sqrt[(p)^(2)- (y)^(2)])^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-  
|-  
| [https://dlmf.nist.gov/19.22.E7 19.22.E7] || [[Item:Q6445|<math>2p^{2}\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = v_{+}v_{-}\CarlsonsymellintRJ@{0}{xy}{a^{2}}{v^{2}_{+}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2p^{2}\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = v_{+}v_{-}\CarlsonsymellintRJ@{0}{xy}{a^{2}}{v^{2}_{+}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}</syntaxhighlight> || <math>v_{+} = (p^{2}+ xy)/(2p), v_{-} = (p^{2}- xy)/(2p)</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*(p)^(2)* 3*((y)^(2)-0)/((y)^(2)-(p)^(2))*(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == Subscript[v, +]*Subscript[v, -]*3*((a)^(2)-0)/((a)^(2)-(Subscript[v, +])^(2))*(EllipticPi[((a)^(2)-(Subscript[v, +])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]+ 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]</syntaxhighlight> || Missing Macro Error || Failure || - || Error
| [https://dlmf.nist.gov/19.22.E7 19.22.E7] || <math qid="Q6445">2p^{2}\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = v_{+}v_{-}\CarlsonsymellintRJ@{0}{xy}{a^{2}}{v^{2}_{+}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2p^{2}\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = v_{+}v_{-}\CarlsonsymellintRJ@{0}{xy}{a^{2}}{v^{2}_{+}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}</syntaxhighlight> || <math>v_{+} = (p^{2}+ xy)/(2p), v_{-} = (p^{2}- xy)/(2p)</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*(p)^(2)* 3*((y)^(2)-0)/((y)^(2)-(p)^(2))*(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == Subscript[v, +]*Subscript[v, -]*3*((a)^(2)-0)/((a)^(2)-(Subscript[v, +])^(2))*(EllipticPi[((a)^(2)-(Subscript[v, +])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]+ 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]</syntaxhighlight> || Missing Macro Error || Failure || - || Error
|-  
|-  
| [https://dlmf.nist.gov/19.22.E8 19.22.E8] || [[Item:Q6446|<math>\frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} = \frac{1}{\AGM@{a_{0}}{g_{0}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} = \frac{1}{\AGM@{a_{0}}{g_{0}}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(2)/(Pi)*0.5*int(1/(sqrt(t+0)*sqrt(t+(a[0])^(2))*sqrt(t+(g[0])^(2))), t = 0..infinity) = (1)/(GaussAGM(a[0], g[0]))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Aborted || Missing Macro Error || Skipped - Because timed out || -
| [https://dlmf.nist.gov/19.22.E8 19.22.E8] || <math qid="Q6446">\frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} = \frac{1}{\AGM@{a_{0}}{g_{0}}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} = \frac{1}{\AGM@{a_{0}}{g_{0}}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(2)/(Pi)*0.5*int(1/(sqrt(t+0)*sqrt(t+(a[0])^(2))*sqrt(t+(g[0])^(2))), t = 0..infinity) = (1)/(GaussAGM(a[0], g[0]))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Aborted || Missing Macro Error || Skipped - Because timed out || -
|-  
|-  
| [https://dlmf.nist.gov/19.22.E9 19.22.E9] || [[Item:Q6447|<math>\frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{0}^{2}-\sum_{n=0}^{\infty}2^{n-1}c_{n}^{2}\right) = \frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{1}^{2}-\sum_{n=2}^{\infty}2^{n-1}c_{n}^{2}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{0}^{2}-\sum_{n=0}^{\infty}2^{n-1}c_{n}^{2}\right) = \frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{1}^{2}-\sum_{n=2}^{\infty}2^{n-1}c_{n}^{2}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(GaussAGM(a[0], g[0]))*((a[0])^(2)- sum((2)^(n - 1)* (c[n])^(2), n = 0..infinity)) = (1)/(GaussAGM(a[0], g[0]))*((a[1])^(2)- sum((2)^(n - 1)* (c[n])^(2), n = 2..infinity))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Error || -
| [https://dlmf.nist.gov/19.22.E9 19.22.E9] || <math qid="Q6447">\frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{0}^{2}-\sum_{n=0}^{\infty}2^{n-1}c_{n}^{2}\right) = \frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{1}^{2}-\sum_{n=2}^{\infty}2^{n-1}c_{n}^{2}\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{0}^{2}-\sum_{n=0}^{\infty}2^{n-1}c_{n}^{2}\right) = \frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{1}^{2}-\sum_{n=2}^{\infty}2^{n-1}c_{n}^{2}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(GaussAGM(a[0], g[0]))*((a[0])^(2)- sum((2)^(n - 1)* (c[n])^(2), n = 0..infinity)) = (1)/(GaussAGM(a[0], g[0]))*((a[1])^(2)- sum((2)^(n - 1)* (c[n])^(2), n = 2..infinity))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Error || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex5 19.22#Ex5] || [[Item:Q6449|<math>Q_{0} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Q_{0} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Q[0] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Q, 0] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex5 19.22#Ex5] || <math qid="Q6449">Q_{0} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Q_{0} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Q[0] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Q, 0] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex6 19.22#Ex6] || [[Item:Q6450|<math>Q_{n+1} = \tfrac{1}{2}Q_{n}\frac{a_{n}-g_{n}}{a_{n}+g_{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Q_{n+1} = \tfrac{1}{2}Q_{n}\frac{a_{n}-g_{n}}{a_{n}+g_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Q[n + 1] = (1)/(2)*Q[n]*(a[n]- g[n])/(a[n]+ g[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Q, n + 1] == Divide[1,2]*Subscript[Q, n]*Divide[Subscript[a, n]- Subscript[g, n],Subscript[a, n]+ Subscript[g, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex6 19.22#Ex6] || <math qid="Q6450">Q_{n+1} = \tfrac{1}{2}Q_{n}\frac{a_{n}-g_{n}}{a_{n}+g_{n}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Q_{n+1} = \tfrac{1}{2}Q_{n}\frac{a_{n}-g_{n}}{a_{n}+g_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Q[n + 1] = (1)/(2)*Q[n]*(a[n]- g[n])/(a[n]+ g[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Q, n + 1] == Divide[1,2]*Subscript[Q, n]*Divide[Subscript[a, n]- Subscript[g, n],Subscript[a, n]+ Subscript[g, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex7 19.22#Ex7] || [[Item:Q6452|<math>p_{n+1} = \frac{p_{n}^{2}+a_{n}g_{n}}{2p_{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{n+1} = \frac{p_{n}^{2}+a_{n}g_{n}}{2p_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">p[n + 1] = ((p[n])^(2)+ a[n]*g[n])/(2*p[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[p, n + 1] == Divide[(Subscript[p, n])^(2)+ Subscript[a, n]*Subscript[g, n],2*Subscript[p, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex7 19.22#Ex7] || <math qid="Q6452">p_{n+1} = \frac{p_{n}^{2}+a_{n}g_{n}}{2p_{n}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{n+1} = \frac{p_{n}^{2}+a_{n}g_{n}}{2p_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">p[n + 1] = ((p[n])^(2)+ a[n]*g[n])/(2*p[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[p, n + 1] == Divide[(Subscript[p, n])^(2)+ Subscript[a, n]*Subscript[g, n],2*Subscript[p, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex8 19.22#Ex8] || [[Item:Q6453|<math>\varepsilon_{n} = \frac{p_{n}^{2}-a_{n}g_{n}}{p_{n}^{2}+a_{n}g_{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\varepsilon_{n} = \frac{p_{n}^{2}-a_{n}g_{n}}{p_{n}^{2}+a_{n}g_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">varepsilon[n] = ((p[n])^(2)- a[n]*g[n])/((p[n])^(2)+ a[n]*g[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[CurlyEpsilon], n] == Divide[(Subscript[p, n])^(2)- Subscript[a, n]*Subscript[g, n],(Subscript[p, n])^(2)+ Subscript[a, n]*Subscript[g, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex8 19.22#Ex8] || <math qid="Q6453">\varepsilon_{n} = \frac{p_{n}^{2}-a_{n}g_{n}}{p_{n}^{2}+a_{n}g_{n}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\varepsilon_{n} = \frac{p_{n}^{2}-a_{n}g_{n}}{p_{n}^{2}+a_{n}g_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">varepsilon[n] = ((p[n])^(2)- a[n]*g[n])/((p[n])^(2)+ a[n]*g[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[CurlyEpsilon], n] == Divide[(Subscript[p, n])^(2)- Subscript[a, n]*Subscript[g, n],(Subscript[p, n])^(2)+ Subscript[a, n]*Subscript[g, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex9 19.22#Ex9] || [[Item:Q6454|<math>Q_{0} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Q_{0} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Q[0] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Q, 0] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex9 19.22#Ex9] || <math qid="Q6454">Q_{0} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Q_{0} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Q[0] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Q, 0] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex10 19.22#Ex10] || [[Item:Q6455|<math>Q_{n+1} = \tfrac{1}{2}Q_{n}\varepsilon_{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Q_{n+1} = \tfrac{1}{2}Q_{n}\varepsilon_{n}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Q[n + 1] = (1)/(2)*Q[n]*varepsilon[n]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Q, n + 1] == Divide[1,2]*Subscript[Q, n]*Subscript[\[CurlyEpsilon], n]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex10 19.22#Ex10] || <math qid="Q6455">Q_{n+1} = \tfrac{1}{2}Q_{n}\varepsilon_{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Q_{n+1} = \tfrac{1}{2}Q_{n}\varepsilon_{n}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Q[n + 1] = (1)/(2)*Q[n]*varepsilon[n]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Q, n + 1] == Divide[1,2]*Subscript[Q, n]*Subscript[\[CurlyEpsilon], n]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22.E15 19.22.E15] || [[Item:Q6457|<math>p_{0}^{2} = a_{0}^{2}(q_{0}^{2}+g_{0}^{2})/(q_{0}^{2}+a_{0}^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{0}^{2} = a_{0}^{2}(q_{0}^{2}+g_{0}^{2})/(q_{0}^{2}+a_{0}^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(p[0])^(2) = (a[0])^(2)*((q[0])^(2)+ (g[0])^(2))/((q[0])^(2)+ (a[0])^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[p, 0])^(2) == (Subscript[a, 0])^(2)*((Subscript[q, 0])^(2)+ (Subscript[g, 0])^(2))/((Subscript[q, 0])^(2)+ (Subscript[a, 0])^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22.E15 19.22.E15] || <math qid="Q6457">p_{0}^{2} = a_{0}^{2}(q_{0}^{2}+g_{0}^{2})/(q_{0}^{2}+a_{0}^{2})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{0}^{2} = a_{0}^{2}(q_{0}^{2}+g_{0}^{2})/(q_{0}^{2}+a_{0}^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(p[0])^(2) = (a[0])^(2)*((q[0])^(2)+ (g[0])^(2))/((q[0])^(2)+ (a[0])^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[p, 0])^(2) == (Subscript[a, 0])^(2)*((Subscript[q, 0])^(2)+ (Subscript[g, 0])^(2))/((Subscript[q, 0])^(2)+ (Subscript[a, 0])^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex11 19.22#Ex11] || [[Item:Q6458|<math>a = (x+y)/2</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a = (x+y)/2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a = (x + y)/2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a == (x + y)/2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex11 19.22#Ex11] || <math qid="Q6458">a = (x+y)/2</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a = (x+y)/2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a = (x + y)/2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a == (x + y)/2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex12 19.22#Ex12] || [[Item:Q6459|<math>2z_{+} = \sqrt{(z+x)(z+y)}+\sqrt{(z-x)(z-y)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>2z_{+} = \sqrt{(z+x)(z+y)}+\sqrt{(z-x)(z-y)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">2*x + y*I[+] = sqrt(((x + y*I)+ x)*((x + y*I)+ y))+sqrt(((x + y*I)- x)*((x + y*I)- y))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">2*Subscript[x + y*I, +] == Sqrt[((x + y*I)+ x)*((x + y*I)+ y)]+Sqrt[((x + y*I)- x)*((x + y*I)- y)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex12 19.22#Ex12] || <math qid="Q6459">2z_{+} = \sqrt{(z+x)(z+y)}+\sqrt{(z-x)(z-y)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>2z_{+} = \sqrt{(z+x)(z+y)}+\sqrt{(z-x)(z-y)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">2*x + y*I[+] = sqrt(((x + y*I)+ x)*((x + y*I)+ y))+sqrt(((x + y*I)- x)*((x + y*I)- y))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">2*Subscript[x + y*I, +] == Sqrt[((x + y*I)+ x)*((x + y*I)+ y)]+Sqrt[((x + y*I)- x)*((x + y*I)- y)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex13 19.22#Ex13] || [[Item:Q6460|<math>z_{+}z_{-} = za</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{+}z_{-} = za</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[+]*z[-] = z*a</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, +]*Subscript[z, -] == z*a</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex13 19.22#Ex13] || <math qid="Q6460">z_{+}z_{-} = za</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{+}z_{-} = za</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[+]*z[-] = z*a</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, +]*Subscript[z, -] == z*a</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex14 19.22#Ex14] || [[Item:Q6461|<math>z_{+}^{2}+z_{-}^{2} = z^{2}+xy</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{+}^{2}+z_{-}^{2} = z^{2}+xy</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(x + y*I[+])^(2)+(x + y*I[-])^(2) = (x + y*I)^(2)+ x*y</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[x + y*I, +])^(2)+(Subscript[x + y*I, -])^(2) == (x + y*I)^(2)+ x*y</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex14 19.22#Ex14] || <math qid="Q6461">z_{+}^{2}+z_{-}^{2} = z^{2}+xy</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{+}^{2}+z_{-}^{2} = z^{2}+xy</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(x + y*I[+])^(2)+(x + y*I[-])^(2) = (x + y*I)^(2)+ x*y</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[x + y*I, +])^(2)+(Subscript[x + y*I, -])^(2) == (x + y*I)^(2)+ x*y</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex15 19.22#Ex15] || [[Item:Q6462|<math>z_{+}^{2}-z_{-}^{2} = \sqrt{(z^{2}-x^{2})(z^{2}-y^{2})}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{+}^{2}-z_{-}^{2} = \sqrt{(z^{2}-x^{2})(z^{2}-y^{2})}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(x + y*I[+])^(2)-(x + y*I[-])^(2) = sqrt(((x + y*I)^(2)- (x)^(2))*((x + y*I)^(2)- (y)^(2)))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2) == Sqrt[((x + y*I)^(2)- (x)^(2))*((x + y*I)^(2)- (y)^(2))]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex15 19.22#Ex15] || <math qid="Q6462">z_{+}^{2}-z_{-}^{2} = \sqrt{(z^{2}-x^{2})(z^{2}-y^{2})}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{+}^{2}-z_{-}^{2} = \sqrt{(z^{2}-x^{2})(z^{2}-y^{2})}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(x + y*I[+])^(2)-(x + y*I[-])^(2) = sqrt(((x + y*I)^(2)- (x)^(2))*((x + y*I)^(2)- (y)^(2)))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2) == Sqrt[((x + y*I)^(2)- (x)^(2))*((x + y*I)^(2)- (y)^(2))]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex16 19.22#Ex16] || [[Item:Q6463|<math>4(z_{+}^{2}-a^{2}) = (\sqrt{z^{2}-x^{2}}+\sqrt{z^{2}-y^{2}})^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>4(z_{+}^{2}-a^{2}) = (\sqrt{z^{2}-x^{2}}+\sqrt{z^{2}-y^{2}})^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">4*((x + y*I[+])^(2)- (a)^(2)) = (sqrt((x + y*I)^(2)- (x)^(2))+sqrt((x + y*I)^(2)- (y)^(2)))^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">4*((Subscript[x + y*I, +])^(2)- (a)^(2)) == (Sqrt[(x + y*I)^(2)- (x)^(2)]+Sqrt[(x + y*I)^(2)- (y)^(2)])^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex16 19.22#Ex16] || <math qid="Q6463">4(z_{+}^{2}-a^{2}) = (\sqrt{z^{2}-x^{2}}+\sqrt{z^{2}-y^{2}})^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>4(z_{+}^{2}-a^{2}) = (\sqrt{z^{2}-x^{2}}+\sqrt{z^{2}-y^{2}})^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">4*((x + y*I[+])^(2)- (a)^(2)) = (sqrt((x + y*I)^(2)- (x)^(2))+sqrt((x + y*I)^(2)- (y)^(2)))^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">4*((Subscript[x + y*I, +])^(2)- (a)^(2)) == (Sqrt[(x + y*I)^(2)- (x)^(2)]+Sqrt[(x + y*I)^(2)- (y)^(2)])^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-  
|-  
| [https://dlmf.nist.gov/19.22.E18 19.22.E18] || [[Item:Q6464|<math>\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}} = \CarlsonsymellintRF@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}} = \CarlsonsymellintRF@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>0.5*int(1/(sqrt(t+(x)^(2))*sqrt(t+(y)^(2))*sqrt(t+(x + y*I)^(2))), t = 0..infinity) = 0.5*int(1/(sqrt(t+(a)^(2))*sqrt(t+(x + y*I[-])^(2))*sqrt(t+(x + y*I[+])^(2))), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)] == EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, +])^(2)]],((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))/((Subscript[x + y*I, +])^(2)-(a)^(2))]/Sqrt[(Subscript[x + y*I, +])^(2)-(a)^(2)]</syntaxhighlight> || Error || Failure || - || Error
| [https://dlmf.nist.gov/19.22.E18 19.22.E18] || <math qid="Q6464">\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}} = \CarlsonsymellintRF@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}} = \CarlsonsymellintRF@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>0.5*int(1/(sqrt(t+(x)^(2))*sqrt(t+(y)^(2))*sqrt(t+(x + y*I)^(2))), t = 0..infinity) = 0.5*int(1/(sqrt(t+(a)^(2))*sqrt(t+(x + y*I[-])^(2))*sqrt(t+(x + y*I[+])^(2))), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)] == EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, +])^(2)]],((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))/((Subscript[x + y*I, +])^(2)-(a)^(2))]/Sqrt[(Subscript[x + y*I, +])^(2)-(a)^(2)]</syntaxhighlight> || Error || Failure || - || Error
|-  
|-  
| [https://dlmf.nist.gov/19.22.E19 19.22.E19] || [[Item:Q6465|<math>(z_{+}^{2}-z_{-}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{+}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(z_{+}^{2}-z_{-}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{+}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))*3*(EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-EllipticE[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))])/(((x + y*I)^(2)-(y)^(2))*((x + y*I)^(2)-(x)^(2))^(1/2)) == 2*((Subscript[x + y*I, +])^(2)- (a)^(2))*3*(EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, +])^(2)]],((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))/((Subscript[x + y*I, +])^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, +])^(2)]],((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))/((Subscript[x + y*I, +])^(2)-(a)^(2))])/(((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))*((Subscript[x + y*I, +])^(2)-(a)^(2))^(1/2))- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+(3/(x + y*I))</syntaxhighlight> || Missing Macro Error || Failure || - || Error
| [https://dlmf.nist.gov/19.22.E19 19.22.E19] || <math qid="Q6465">(z_{+}^{2}-z_{-}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{+}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(z_{+}^{2}-z_{-}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{+}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))*3*(EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-EllipticE[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))])/(((x + y*I)^(2)-(y)^(2))*((x + y*I)^(2)-(x)^(2))^(1/2)) == 2*((Subscript[x + y*I, +])^(2)- (a)^(2))*3*(EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, +])^(2)]],((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))/((Subscript[x + y*I, +])^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, +])^(2)]],((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))/((Subscript[x + y*I, +])^(2)-(a)^(2))])/(((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))*((Subscript[x + y*I, +])^(2)-(a)^(2))^(1/2))- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+(3/(x + y*I))</syntaxhighlight> || Missing Macro Error || Failure || - || Error
|-  
|-  
| [https://dlmf.nist.gov/19.22.E19 19.22.E19] || [[Item:Q6465|<math>(z_{-}^{2}-z_{+}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{-}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(z_{-}^{2}-z_{+}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{-}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))*3*(EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-EllipticE[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))])/(((x + y*I)^(2)-(y)^(2))*((x + y*I)^(2)-(x)^(2))^(1/2)) == 2*((Subscript[x + y*I, -])^(2)- (a)^(2))*3*(EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))])/(((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))*((Subscript[x + y*I, -])^(2)-(a)^(2))^(1/2))- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+(3/(x + y*I))</syntaxhighlight> || Missing Macro Error || Failure || - || Error
| [https://dlmf.nist.gov/19.22.E19 19.22.E19] || <math qid="Q6465">(z_{-}^{2}-z_{+}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{-}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(z_{-}^{2}-z_{+}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{-}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))*3*(EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-EllipticE[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))])/(((x + y*I)^(2)-(y)^(2))*((x + y*I)^(2)-(x)^(2))^(1/2)) == 2*((Subscript[x + y*I, -])^(2)- (a)^(2))*3*(EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))])/(((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))*((Subscript[x + y*I, -])^(2)-(a)^(2))^(1/2))- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+(3/(x + y*I))</syntaxhighlight> || Missing Macro Error || Failure || - || Error
|-  
|-  
| [https://dlmf.nist.gov/19.22.E20 19.22.E20] || [[Item:Q6466|<math>(p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>((Subscript[p, +])^(2)- (Subscript[p, -])^(2))*3*((x + y*I)^(2)-(x)^(2))/((x + y*I)^(2)-(p)^(2))*(EllipticPi[((x + y*I)^(2)-(p)^(2))/((x + y*I)^(2)-(x)^(2)),ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))])/Sqrt[(x + y*I)^(2)-(x)^(2)] == 2*((Subscript[p, +])^(2)- (a)^(2))*3*((Subscript[x + y*I, -])^(2)-(a)^(2))/((Subscript[x + y*I, -])^(2)-(Subscript[p, +])^(2))*(EllipticPi[((Subscript[x + y*I, -])^(2)-(Subscript[p, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2)),ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))])/Sqrt[(Subscript[x + y*I, -])^(2)-(a)^(2)]- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+ 3*1/Sqrt[(p)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x + y*I)^(2))/((p)^(2))]</syntaxhighlight> || Missing Macro Error || Failure || - || Error
| [https://dlmf.nist.gov/19.22.E20 19.22.E20] || <math qid="Q6466">(p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>((Subscript[p, +])^(2)- (Subscript[p, -])^(2))*3*((x + y*I)^(2)-(x)^(2))/((x + y*I)^(2)-(p)^(2))*(EllipticPi[((x + y*I)^(2)-(p)^(2))/((x + y*I)^(2)-(x)^(2)),ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))])/Sqrt[(x + y*I)^(2)-(x)^(2)] == 2*((Subscript[p, +])^(2)- (a)^(2))*3*((Subscript[x + y*I, -])^(2)-(a)^(2))/((Subscript[x + y*I, -])^(2)-(Subscript[p, +])^(2))*(EllipticPi[((Subscript[x + y*I, -])^(2)-(Subscript[p, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2)),ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))])/Sqrt[(Subscript[x + y*I, -])^(2)-(a)^(2)]- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+ 3*1/Sqrt[(p)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x + y*I)^(2))/((p)^(2))]</syntaxhighlight> || Missing Macro Error || Failure || - || Error
|-  
|-  
| [https://dlmf.nist.gov/19.22.E20 19.22.E20] || [[Item:Q6466|<math>(p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>((Subscript[p, -])^(2)- (Subscript[p, +])^(2))*3*((x + y*I)^(2)-(x)^(2))/((x + y*I)^(2)-(p)^(2))*(EllipticPi[((x + y*I)^(2)-(p)^(2))/((x + y*I)^(2)-(x)^(2)),ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))])/Sqrt[(x + y*I)^(2)-(x)^(2)] == 2*((Subscript[p, -])^(2)- (a)^(2))*3*((Subscript[x + y*I, -])^(2)-(a)^(2))/((Subscript[x + y*I, -])^(2)-(Subscript[p, -])^(2))*(EllipticPi[((Subscript[x + y*I, -])^(2)-(Subscript[p, -])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2)),ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))])/Sqrt[(Subscript[x + y*I, -])^(2)-(a)^(2)]- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+ 3*1/Sqrt[(p)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x + y*I)^(2))/((p)^(2))]</syntaxhighlight> || Missing Macro Error || Failure || - || Error
| [https://dlmf.nist.gov/19.22.E20 19.22.E20] || <math qid="Q6466">(p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>((Subscript[p, -])^(2)- (Subscript[p, +])^(2))*3*((x + y*I)^(2)-(x)^(2))/((x + y*I)^(2)-(p)^(2))*(EllipticPi[((x + y*I)^(2)-(p)^(2))/((x + y*I)^(2)-(x)^(2)),ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))])/Sqrt[(x + y*I)^(2)-(x)^(2)] == 2*((Subscript[p, -])^(2)- (a)^(2))*3*((Subscript[x + y*I, -])^(2)-(a)^(2))/((Subscript[x + y*I, -])^(2)-(Subscript[p, -])^(2))*(EllipticPi[((Subscript[x + y*I, -])^(2)-(Subscript[p, -])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2)),ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))])/Sqrt[(Subscript[x + y*I, -])^(2)-(a)^(2)]- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+ 3*1/Sqrt[(p)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x + y*I)^(2))/((p)^(2))]</syntaxhighlight> || Missing Macro Error || Failure || - || Error
|-  
|-  
| [https://dlmf.nist.gov/19.22.E21 19.22.E21] || [[Item:Q6467|<math>2\CarlsonsymellintRG@{x^{2}}{y^{2}}{z^{2}} = 4\CarlsonsymellintRG@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-xy\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}-z</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2\CarlsonsymellintRG@{x^{2}}{y^{2}}{z^{2}} = 4\CarlsonsymellintRG@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-xy\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}-z</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*Sqrt[(x + y*I)^(2)-(x)^(2)]*(EllipticE[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]+(Cot[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]]])^2*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]+Cot[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]]]^2]) == 4*Sqrt[(Subscript[x + y*I, -])^(2)-(a)^(2)]*(EllipticE[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]+(Cot[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]]])^2*EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]+Cot[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]]]^2])- x*y*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]-(x + y*I)</syntaxhighlight> || Missing Macro Error || Failure || - || Error
| [https://dlmf.nist.gov/19.22.E21 19.22.E21] || <math qid="Q6467">2\CarlsonsymellintRG@{x^{2}}{y^{2}}{z^{2}} = 4\CarlsonsymellintRG@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-xy\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}-z</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2\CarlsonsymellintRG@{x^{2}}{y^{2}}{z^{2}} = 4\CarlsonsymellintRG@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-xy\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}-z</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*Sqrt[(x + y*I)^(2)-(x)^(2)]*(EllipticE[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]+(Cot[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]]])^2*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]+Cot[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]]]^2]) == 4*Sqrt[(Subscript[x + y*I, -])^(2)-(a)^(2)]*(EllipticE[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]+(Cot[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]]])^2*EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]+Cot[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]]]^2])- x*y*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]-(x + y*I)</syntaxhighlight> || Missing Macro Error || Failure || - || Error
|-  
|-  
| [https://dlmf.nist.gov/19.22.E22 19.22.E22] || [[Item:Q6468|<math>\CarlsonellintRC@{x^{2}}{y^{2}} = \CarlsonellintRC@{a^{2}}{ay}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonellintRC@{x^{2}}{y^{2}} = \CarlsonellintRC@{a^{2}}{ay}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((y)^(2))] == 1/Sqrt[a*y]*Hypergeometric2F1[1/2,1/2,3/2,1-((a)^(2))/(a*y)]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [108 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
| [https://dlmf.nist.gov/19.22.E22 19.22.E22] || <math qid="Q6468">\CarlsonellintRC@{x^{2}}{y^{2}} = \CarlsonellintRC@{a^{2}}{ay}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonellintRC@{x^{2}}{y^{2}} = \CarlsonellintRC@{a^{2}}{ay}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((y)^(2))] == 1/Sqrt[a*y]*Hypergeometric2F1[1/2,1/2,3/2,1-((a)^(2))/(a*y)]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [108 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex17 19.22#Ex17] || [[Item:Q6469|<math>x+y = 2a</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x+y = 2a</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x + y = 2*a</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x + y == 2*a</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex17 19.22#Ex17] || <math qid="Q6469">x+y = 2a</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x+y = 2a</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x + y = 2*a</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x + y == 2*a</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex18 19.22#Ex18] || [[Item:Q6470|<math>x-y = (\ifrac{2}{a})\sqrt{(a^{2}-z_{+}^{2})(a^{2}-z_{-}^{2})}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x-y = (\ifrac{2}{a})\sqrt{(a^{2}-z_{+}^{2})(a^{2}-z_{-}^{2})}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x - y = ((2)/(a))*sqrt(((a)^(2)-(x + y*I[+])^(2))*((a)^(2)-(x + y*I[-])^(2)))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x - y == (Divide[2,a])*Sqrt[((a)^(2)-(Subscript[x + y*I, +])^(2))*((a)^(2)-(Subscript[x + y*I, -])^(2))]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex18 19.22#Ex18] || <math qid="Q6470">x-y = (\ifrac{2}{a})\sqrt{(a^{2}-z_{+}^{2})(a^{2}-z_{-}^{2})}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x-y = (\ifrac{2}{a})\sqrt{(a^{2}-z_{+}^{2})(a^{2}-z_{-}^{2})}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x - y = ((2)/(a))*sqrt(((a)^(2)-(x + y*I[+])^(2))*((a)^(2)-(x + y*I[-])^(2)))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x - y == (Divide[2,a])*Sqrt[((a)^(2)-(Subscript[x + y*I, +])^(2))*((a)^(2)-(Subscript[x + y*I, -])^(2))]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/19.22#Ex19 19.22#Ex19] || [[Item:Q6471|<math>z = \ifrac{z_{+}z_{-}}{a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = \ifrac{z_{+}z_{-}}{a}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = (z[+]*z[-])/(a)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == Divide[Subscript[z, +]*Subscript[z, -],a]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/19.22#Ex19 19.22#Ex19] || <math qid="Q6471">z = \ifrac{z_{+}z_{-}}{a}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = \ifrac{z_{+}z_{-}}{a}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = (z[+]*z[-])/(a)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == Divide[Subscript[z, +]*Subscript[z, -],a]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|}
|}
</div>
</div>

Latest revision as of 12:52, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple
Symbolic
Mathematica
Numeric
Maple
Numeric
Mathematica
19.22.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{0}{x^{2}}{y^{2}} = \CarlsonsymellintRF@{0}{xy}{a^{2}}}
\CarlsonsymellintRF@{0}{x^{2}}{y^{2}} = \CarlsonsymellintRF@{0}{xy}{a^{2}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
0.5*int(1/(sqrt(t+0)*sqrt(t+(x)^(2))*sqrt(t+(y)^(2))), t = 0..infinity) = 0.5*int(1/(sqrt(t+0)*sqrt(t+x*y)*sqrt(t+(a)^(2))), t = 0..infinity)
EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]/Sqrt[(y)^(2)-0] == EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]
Aborted Failure Skipped - Because timed out
Failed [102 / 108]
Result: Complex[0.1731783664325578, 0.8740191847640398]
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}

Result: Complex[0.4406854652170371, 0.9732684211375591]
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -0.5]}

... skip entries to safe data
19.22.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRG@{0}{x^{2}}{y^{2}} = 4\CarlsonsymellintRG@{0}{xy}{a^{2}}-xy\CarlsonsymellintRF@{0}{xy}{a^{2}}}
2\CarlsonsymellintRG@{0}{x^{2}}{y^{2}} = 4\CarlsonsymellintRG@{0}{xy}{a^{2}}-xy\CarlsonsymellintRF@{0}{xy}{a^{2}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
Error
2*Sqrt[(y)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(y)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]+Cot[ArcCos[Sqrt[0/(y)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(y)^(2)]]]^2]) == 4*Sqrt[(a)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(a)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]+Cot[ArcCos[Sqrt[0/(a)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(a)^(2)]]]^2])- x*y*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]
Missing Macro Error Failure -
Failed [108 / 108]
Result: Complex[-0.848574889541176, -1.6278775384876862]
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}

Result: -2.356194490192345
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]}

... skip entries to safe data
19.22.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2y^{2}\CarlsonsymellintRD@{0}{x^{2}}{y^{2}} = \tfrac{1}{4}(y^{2}-x^{2})\CarlsonsymellintRD@{0}{xy}{a^{2}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}}
2y^{2}\CarlsonsymellintRD@{0}{x^{2}}{y^{2}} = \tfrac{1}{4}(y^{2}-x^{2})\CarlsonsymellintRD@{0}{xy}{a^{2}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
Error
2*(y)^(2)* 3*(EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/(((y)^(2)-(x)^(2))*((y)^(2)-0)^(1/2)) == Divide[1,4]*((y)^(2)- (x)^(2))*3*(EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/(((a)^(2)-x*y)*((a)^(2)-0)^(1/2))+ 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]
Missing Macro Error Failure -
Failed [108 / 108]
Result: Indeterminate
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}

Result: Indeterminate
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]}

... skip entries to safe data
19.22.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)}
(p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
Error
((Subscript[p, +])^(2)- (Subscript[p, -])^(2))*3*((y)^(2)-0)/((y)^(2)-(p)^(2))*(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == 2*((Subscript[p, +])^(2)- (a)^(2))*3*((a)^(2)-0)/((a)^(2)-(Subscript[p, +])^(2))*(EllipticPi[((a)^(2)-(Subscript[p, +])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]- 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]+ 3*Pi/(2*p)
Missing Macro Error Failure - Error
19.22.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)}
(p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
Error
((Subscript[p, -])^(2)- (Subscript[p, +])^(2))*3*((y)^(2)-0)/((y)^(2)-(p)^(2))*(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == 2*((Subscript[p, -])^(2)- (a)^(2))*3*((a)^(2)-0)/((a)^(2)-(Subscript[p, -])^(2))*(EllipticPi[((a)^(2)-(Subscript[p, -])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]- 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]+ 3*Pi/(2*p)
Missing Macro Error Failure - Error
19.22#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{+}p_{-} = pa}
p_{+}p_{-} = pa
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
p[+]*p[-] = p*a
Subscript[p, +]*Subscript[p, -] == p*a
Skipped - no semantic math Skipped - no semantic math - -
19.22#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{+}^{2}+p_{-}^{2} = p^{2}+xy}
p_{+}^{2}+p_{-}^{2} = p^{2}+xy
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
(p[+])^(2)+ (p[-])^(2) = (p)^(2)+ x*y
(Subscript[p, +])^(2)+ (Subscript[p, -])^(2) == (p)^(2)+ x*y
Skipped - no semantic math Skipped - no semantic math - -
19.22#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{+}^{2}-p_{-}^{2} = \sqrt{(p^{2}-x^{2})(p^{2}-y^{2})}}
p_{+}^{2}-p_{-}^{2} = \sqrt{(p^{2}-x^{2})(p^{2}-y^{2})}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
(p[+])^(2)- (p[-])^(2) = sqrt(((p)^(2)- (x)^(2))*((p)^(2)- (y)^(2)))
(Subscript[p, +])^(2)- (Subscript[p, -])^(2) == Sqrt[((p)^(2)- (x)^(2))*((p)^(2)- (y)^(2))]
Skipped - no semantic math Skipped - no semantic math - -
19.22#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 4(p_{+}^{2}-a^{2}) = (\sqrt{p^{2}-x^{2}}+\sqrt{p^{2}-y^{2}})^{2}}
4(p_{+}^{2}-a^{2}) = (\sqrt{p^{2}-x^{2}}+\sqrt{p^{2}-y^{2}})^{2}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
4*((p[+])^(2)- (a)^(2)) = (sqrt((p)^(2)- (x)^(2))+sqrt((p)^(2)- (y)^(2)))^(2)
4*((Subscript[p, +])^(2)- (a)^(2)) == (Sqrt[(p)^(2)- (x)^(2)]+Sqrt[(p)^(2)- (y)^(2)])^(2)
Skipped - no semantic math Skipped - no semantic math - -
19.22.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2p^{2}\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = v_{+}v_{-}\CarlsonsymellintRJ@{0}{xy}{a^{2}}{v^{2}_{+}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}}
2p^{2}\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = v_{+}v_{-}\CarlsonsymellintRJ@{0}{xy}{a^{2}}{v^{2}_{+}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle v_{+} = (p^{2}+ xy)/(2p), v_{-} = (p^{2}- xy)/(2p)}
Error
2*(p)^(2)* 3*((y)^(2)-0)/((y)^(2)-(p)^(2))*(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == Subscript[v, +]*Subscript[v, -]*3*((a)^(2)-0)/((a)^(2)-(Subscript[v, +])^(2))*(EllipticPi[((a)^(2)-(Subscript[v, +])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]+ 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]
Missing Macro Error Failure - Error
19.22.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} = \frac{1}{\AGM@{a_{0}}{g_{0}}}}
\frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} = \frac{1}{\AGM@{a_{0}}{g_{0}}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
(2)/(Pi)*0.5*int(1/(sqrt(t+0)*sqrt(t+(a[0])^(2))*sqrt(t+(g[0])^(2))), t = 0..infinity) = (1)/(GaussAGM(a[0], g[0]))
Error
Aborted Missing Macro Error Skipped - Because timed out -
19.22.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{0}^{2}-\sum_{n=0}^{\infty}2^{n-1}c_{n}^{2}\right) = \frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{1}^{2}-\sum_{n=2}^{\infty}2^{n-1}c_{n}^{2}\right)}
\frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{0}^{2}-\sum_{n=0}^{\infty}2^{n-1}c_{n}^{2}\right) = \frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{1}^{2}-\sum_{n=2}^{\infty}2^{n-1}c_{n}^{2}\right)
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
(1)/(GaussAGM(a[0], g[0]))*((a[0])^(2)- sum((2)^(n - 1)* (c[n])^(2), n = 0..infinity)) = (1)/(GaussAGM(a[0], g[0]))*((a[1])^(2)- sum((2)^(n - 1)* (c[n])^(2), n = 2..infinity))
Error
Failure Missing Macro Error Error -
19.22#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{0} = 1}
Q_{0} = 1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
Q[0] = 1
Subscript[Q, 0] == 1
Skipped - no semantic math Skipped - no semantic math - -
19.22#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{n+1} = \tfrac{1}{2}Q_{n}\frac{a_{n}-g_{n}}{a_{n}+g_{n}}}
Q_{n+1} = \tfrac{1}{2}Q_{n}\frac{a_{n}-g_{n}}{a_{n}+g_{n}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
Q[n + 1] = (1)/(2)*Q[n]*(a[n]- g[n])/(a[n]+ g[n])
Subscript[Q, n + 1] == Divide[1,2]*Subscript[Q, n]*Divide[Subscript[a, n]- Subscript[g, n],Subscript[a, n]+ Subscript[g, n]]
Skipped - no semantic math Skipped - no semantic math - -
19.22#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{n+1} = \frac{p_{n}^{2}+a_{n}g_{n}}{2p_{n}}}
p_{n+1} = \frac{p_{n}^{2}+a_{n}g_{n}}{2p_{n}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
p[n + 1] = ((p[n])^(2)+ a[n]*g[n])/(2*p[n])
Subscript[p, n + 1] == Divide[(Subscript[p, n])^(2)+ Subscript[a, n]*Subscript[g, n],2*Subscript[p, n]]
Skipped - no semantic math Skipped - no semantic math - -
19.22#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \varepsilon_{n} = \frac{p_{n}^{2}-a_{n}g_{n}}{p_{n}^{2}+a_{n}g_{n}}}
\varepsilon_{n} = \frac{p_{n}^{2}-a_{n}g_{n}}{p_{n}^{2}+a_{n}g_{n}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
varepsilon[n] = ((p[n])^(2)- a[n]*g[n])/((p[n])^(2)+ a[n]*g[n])
Subscript[\[CurlyEpsilon], n] == Divide[(Subscript[p, n])^(2)- Subscript[a, n]*Subscript[g, n],(Subscript[p, n])^(2)+ Subscript[a, n]*Subscript[g, n]]
Skipped - no semantic math Skipped - no semantic math - -
19.22#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{0} = 1}
Q_{0} = 1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
Q[0] = 1
Subscript[Q, 0] == 1
Skipped - no semantic math Skipped - no semantic math - -
19.22#Ex10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{n+1} = \tfrac{1}{2}Q_{n}\varepsilon_{n}}
Q_{n+1} = \tfrac{1}{2}Q_{n}\varepsilon_{n}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
Q[n + 1] = (1)/(2)*Q[n]*varepsilon[n]
Subscript[Q, n + 1] == Divide[1,2]*Subscript[Q, n]*Subscript[\[CurlyEpsilon], n]
Skipped - no semantic math Skipped - no semantic math - -
19.22.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{0}^{2} = a_{0}^{2}(q_{0}^{2}+g_{0}^{2})/(q_{0}^{2}+a_{0}^{2})}
p_{0}^{2} = a_{0}^{2}(q_{0}^{2}+g_{0}^{2})/(q_{0}^{2}+a_{0}^{2})
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
(p[0])^(2) = (a[0])^(2)*((q[0])^(2)+ (g[0])^(2))/((q[0])^(2)+ (a[0])^(2))
(Subscript[p, 0])^(2) == (Subscript[a, 0])^(2)*((Subscript[q, 0])^(2)+ (Subscript[g, 0])^(2))/((Subscript[q, 0])^(2)+ (Subscript[a, 0])^(2))
Skipped - no semantic math Skipped - no semantic math - -
19.22#Ex11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a = (x+y)/2}
a = (x+y)/2
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
a = (x + y)/2
a == (x + y)/2
Skipped - no semantic math Skipped - no semantic math - -
19.22#Ex12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2z_{+} = \sqrt{(z+x)(z+y)}+\sqrt{(z-x)(z-y)}}
2z_{+} = \sqrt{(z+x)(z+y)}+\sqrt{(z-x)(z-y)}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
2*x + y*I[+] = sqrt(((x + y*I)+ x)*((x + y*I)+ y))+sqrt(((x + y*I)- x)*((x + y*I)- y))
2*Subscript[x + y*I, +] == Sqrt[((x + y*I)+ x)*((x + y*I)+ y)]+Sqrt[((x + y*I)- x)*((x + y*I)- y)]
Skipped - no semantic math Skipped - no semantic math - -
19.22#Ex13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{+}z_{-} = za}
z_{+}z_{-} = za
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
z[+]*z[-] = z*a
Subscript[z, +]*Subscript[z, -] == z*a
Skipped - no semantic math Skipped - no semantic math - -
19.22#Ex14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{+}^{2}+z_{-}^{2} = z^{2}+xy}
z_{+}^{2}+z_{-}^{2} = z^{2}+xy
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
(x + y*I[+])^(2)+(x + y*I[-])^(2) = (x + y*I)^(2)+ x*y
(Subscript[x + y*I, +])^(2)+(Subscript[x + y*I, -])^(2) == (x + y*I)^(2)+ x*y
Skipped - no semantic math Skipped - no semantic math - -
19.22#Ex15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{+}^{2}-z_{-}^{2} = \sqrt{(z^{2}-x^{2})(z^{2}-y^{2})}}
z_{+}^{2}-z_{-}^{2} = \sqrt{(z^{2}-x^{2})(z^{2}-y^{2})}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
(x + y*I[+])^(2)-(x + y*I[-])^(2) = sqrt(((x + y*I)^(2)- (x)^(2))*((x + y*I)^(2)- (y)^(2)))
(Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2) == Sqrt[((x + y*I)^(2)- (x)^(2))*((x + y*I)^(2)- (y)^(2))]
Skipped - no semantic math Skipped - no semantic math - -
19.22#Ex16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 4(z_{+}^{2}-a^{2}) = (\sqrt{z^{2}-x^{2}}+\sqrt{z^{2}-y^{2}})^{2}}
4(z_{+}^{2}-a^{2}) = (\sqrt{z^{2}-x^{2}}+\sqrt{z^{2}-y^{2}})^{2}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
4*((x + y*I[+])^(2)- (a)^(2)) = (sqrt((x + y*I)^(2)- (x)^(2))+sqrt((x + y*I)^(2)- (y)^(2)))^(2)
4*((Subscript[x + y*I, +])^(2)- (a)^(2)) == (Sqrt[(x + y*I)^(2)- (x)^(2)]+Sqrt[(x + y*I)^(2)- (y)^(2)])^(2)
Skipped - no semantic math Skipped - no semantic math - -
19.22.E18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}} = \CarlsonsymellintRF@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}}
\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}} = \CarlsonsymellintRF@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
0.5*int(1/(sqrt(t+(x)^(2))*sqrt(t+(y)^(2))*sqrt(t+(x + y*I)^(2))), t = 0..infinity) = 0.5*int(1/(sqrt(t+(a)^(2))*sqrt(t+(x + y*I[-])^(2))*sqrt(t+(x + y*I[+])^(2))), t = 0..infinity)
EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)] == EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, +])^(2)]],((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))/((Subscript[x + y*I, +])^(2)-(a)^(2))]/Sqrt[(Subscript[x + y*I, +])^(2)-(a)^(2)]
Error Failure - Error
19.22.E19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z_{+}^{2}-z_{-}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{+}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)}
(z_{+}^{2}-z_{-}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{+}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
Error
((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))*3*(EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-EllipticE[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))])/(((x + y*I)^(2)-(y)^(2))*((x + y*I)^(2)-(x)^(2))^(1/2)) == 2*((Subscript[x + y*I, +])^(2)- (a)^(2))*3*(EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, +])^(2)]],((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))/((Subscript[x + y*I, +])^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, +])^(2)]],((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))/((Subscript[x + y*I, +])^(2)-(a)^(2))])/(((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))*((Subscript[x + y*I, +])^(2)-(a)^(2))^(1/2))- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+(3/(x + y*I))
Missing Macro Error Failure - Error
19.22.E19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z_{-}^{2}-z_{+}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{-}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)}
(z_{-}^{2}-z_{+}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{-}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
Error
((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))*3*(EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-EllipticE[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))])/(((x + y*I)^(2)-(y)^(2))*((x + y*I)^(2)-(x)^(2))^(1/2)) == 2*((Subscript[x + y*I, -])^(2)- (a)^(2))*3*(EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))])/(((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))*((Subscript[x + y*I, -])^(2)-(a)^(2))^(1/2))- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+(3/(x + y*I))
Missing Macro Error Failure - Error
19.22.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}}
(p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
Error
((Subscript[p, +])^(2)- (Subscript[p, -])^(2))*3*((x + y*I)^(2)-(x)^(2))/((x + y*I)^(2)-(p)^(2))*(EllipticPi[((x + y*I)^(2)-(p)^(2))/((x + y*I)^(2)-(x)^(2)),ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))])/Sqrt[(x + y*I)^(2)-(x)^(2)] == 2*((Subscript[p, +])^(2)- (a)^(2))*3*((Subscript[x + y*I, -])^(2)-(a)^(2))/((Subscript[x + y*I, -])^(2)-(Subscript[p, +])^(2))*(EllipticPi[((Subscript[x + y*I, -])^(2)-(Subscript[p, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2)),ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))])/Sqrt[(Subscript[x + y*I, -])^(2)-(a)^(2)]- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+ 3*1/Sqrt[(p)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x + y*I)^(2))/((p)^(2))]
Missing Macro Error Failure - Error
19.22.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}}
(p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
Error
((Subscript[p, -])^(2)- (Subscript[p, +])^(2))*3*((x + y*I)^(2)-(x)^(2))/((x + y*I)^(2)-(p)^(2))*(EllipticPi[((x + y*I)^(2)-(p)^(2))/((x + y*I)^(2)-(x)^(2)),ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))])/Sqrt[(x + y*I)^(2)-(x)^(2)] == 2*((Subscript[p, -])^(2)- (a)^(2))*3*((Subscript[x + y*I, -])^(2)-(a)^(2))/((Subscript[x + y*I, -])^(2)-(Subscript[p, -])^(2))*(EllipticPi[((Subscript[x + y*I, -])^(2)-(Subscript[p, -])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2)),ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))])/Sqrt[(Subscript[x + y*I, -])^(2)-(a)^(2)]- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+ 3*1/Sqrt[(p)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x + y*I)^(2))/((p)^(2))]
Missing Macro Error Failure - Error
19.22.E21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRG@{x^{2}}{y^{2}}{z^{2}} = 4\CarlsonsymellintRG@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-xy\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}-z}
2\CarlsonsymellintRG@{x^{2}}{y^{2}}{z^{2}} = 4\CarlsonsymellintRG@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-xy\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}-z
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
Error
2*Sqrt[(x + y*I)^(2)-(x)^(2)]*(EllipticE[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]+(Cot[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]]])^2*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]+Cot[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]]]^2]) == 4*Sqrt[(Subscript[x + y*I, -])^(2)-(a)^(2)]*(EllipticE[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]+(Cot[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]]])^2*EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]+Cot[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]]]^2])- x*y*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]-(x + y*I)
Missing Macro Error Failure - Error
19.22.E22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x^{2}}{y^{2}} = \CarlsonellintRC@{a^{2}}{ay}}
\CarlsonellintRC@{x^{2}}{y^{2}} = \CarlsonellintRC@{a^{2}}{ay}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
Error
1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((y)^(2))] == 1/Sqrt[a*y]*Hypergeometric2F1[1/2,1/2,3/2,1-((a)^(2))/(a*y)]
Missing Macro Error Failure -
Failed [108 / 108]
Result: Indeterminate
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}

Result: Indeterminate
Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]}

... skip entries to safe data
19.22#Ex17 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x+y = 2a}
x+y = 2a
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
x + y = 2*a
x + y == 2*a
Skipped - no semantic math Skipped - no semantic math - -
19.22#Ex18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x-y = (\ifrac{2}{a})\sqrt{(a^{2}-z_{+}^{2})(a^{2}-z_{-}^{2})}}
x-y = (\ifrac{2}{a})\sqrt{(a^{2}-z_{+}^{2})(a^{2}-z_{-}^{2})}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
x - y = ((2)/(a))*sqrt(((a)^(2)-(x + y*I[+])^(2))*((a)^(2)-(x + y*I[-])^(2)))
x - y == (Divide[2,a])*Sqrt[((a)^(2)-(Subscript[x + y*I, +])^(2))*((a)^(2)-(Subscript[x + y*I, -])^(2))]
Skipped - no semantic math Skipped - no semantic math - -
19.22#Ex19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \ifrac{z_{+}z_{-}}{a}}
z = \ifrac{z_{+}z_{-}}{a}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
z = (z[+]*z[-])/(a)
z == Divide[Subscript[z, +]*Subscript[z, -],a]
Skipped - no semantic math Skipped - no semantic math - -