Results of Elliptic Integrals
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| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 19.2.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{k} = \int_{0}^{\phi}\frac{\diff{\theta}}{\sqrt{1-k^{2}\sin^{2}@@{\theta}}}} | EllipticF(sin(phi), k)= int((1)/(sqrt(1 - (k)^(2)* (sin(theta))^(2))), theta = 0..phi) |
EllipticF[\[Phi], (k)^2]= Integrate[Divide[1,Sqrt[1 - (k)^(2)* (Sin[\[Theta]])^(2)]], {\[Theta], 0, \[Phi]}] |
Failure | Failure | Skip | Error |
| 19.2.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\phi}\frac{\diff{\theta}}{\sqrt{1-k^{2}\sin^{2}@@{\theta}}} = \int_{0}^{\sin@@{\phi}}\frac{\diff{t}}{\sqrt{1-t^{2}}\sqrt{1-k^{2}t^{2}}}} | int((1)/(sqrt(1 - (k)^(2)* (sin(theta))^(2))), theta = 0..phi)= int((1)/(sqrt(1 - (t)^(2))*sqrt(1 - (k)^(2)* (t)^(2))), t = 0..sin(phi)) |
Integrate[Divide[1,Sqrt[1 - (k)^(2)* (Sin[\[Theta]])^(2)]], {\[Theta], 0, \[Phi]}]= Integrate[Divide[1,Sqrt[1 - (t)^(2)]*Sqrt[1 - (k)^(2)* (t)^(2)]], {t, 0, Sin[\[Phi]]}] |
Failure | Failure | Skip | Error |
| 19.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\phi}\sqrt{1-k^{2}\sin^{2}@@{\theta}}\diff{\theta}\\ = \int_{0}^{\sin@@{\phi}}\frac{\sqrt{1-k^{2}t^{2}}}{\sqrt{1-t^{2}}}\diff{t}} | int(sqrt(1 - (k)^(2)* (sin(theta))^(2)), theta = 0..phi)= int((sqrt(1 - (k)^(2)* (t)^(2)))/(sqrt(1 - (t)^(2))), t = 0..sin(phi)) |
Integrate[Sqrt[1 - (k)^(2)* (Sin[\[Theta]])^(2)], {\[Theta], 0, \[Phi]}]= Integrate[Divide[Sqrt[1 - (k)^(2)* (t)^(2)],Sqrt[1 - (t)^(2)]], {t, 0, Sin[\[Phi]]}] |
Error | Error | - | - |
| 19.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintDk@{\phi}{k} = \int_{0}^{\phi}\frac{\sin^{2}@@{\theta}\diff{\theta}}{\sqrt{1-k^{2}\sin^{2}@@{\theta}}}} | (EllipticF(sin(phi), k) - EllipticE(sin(phi), k))/(k)^2 = int(((sin(theta))^(2))/(sqrt(1 - (k)^(2)* (sin(theta))^(2))), theta = 0..phi) |
Divide[EllipticF[\[Phi], (k)^2] - EllipticE[\[Phi], (k)^2], (k)^4]= Integrate[Divide[(Sin[\[Theta]])^(2),Sqrt[1 - (k)^(2)* (Sin[\[Theta]])^(2)]], {\[Theta], 0, \[Phi]}] |
Failure | Failure | Skip | Error |
| 19.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\phi}\frac{\sin^{2}@@{\theta}\diff{\theta}}{\sqrt{1-k^{2}\sin^{2}@@{\theta}}} = \int_{0}^{\sin@@{\phi}}\frac{t^{2}\diff{t}}{\sqrt{1-t^{2}}\sqrt{1-k^{2}t^{2}}}} | int(((sin(theta))^(2))/(sqrt(1 - (k)^(2)* (sin(theta))^(2))), theta = 0..phi)= int(((t)^(2))/(sqrt(1 - (t)^(2))*sqrt(1 - (k)^(2)* (t)^(2))), t = 0..sin(phi)) |
Integrate[Divide[(Sin[\[Theta]])^(2),Sqrt[1 - (k)^(2)* (Sin[\[Theta]])^(2)]], {\[Theta], 0, \[Phi]}]= Integrate[Divide[(t)^(2),Sqrt[1 - (t)^(2)]*Sqrt[1 - (k)^(2)* (t)^(2)]], {t, 0, Sin[\[Phi]]}] |
Failure | Failure | Skip | Error |
| 19.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\sin@@{\phi}}\frac{t^{2}\diff{t}}{\sqrt{1-t^{2}}\sqrt{1-k^{2}t^{2}}} = (\incellintFk@{\phi}{k}-\incellintEk@{\phi}{k})/k^{2}} | int(((t)^(2))/(sqrt(1 - (t)^(2))*sqrt(1 - (k)^(2)* (t)^(2))), t = 0..sin(phi))=(EllipticF(sin(phi), k)- EllipticE(sin(phi), k))/ (k)^(2) |
Integrate[Divide[(t)^(2),Sqrt[1 - (t)^(2)]*Sqrt[1 - (k)^(2)* (t)^(2)]], {t, 0, Sin[\[Phi]]}]=(EllipticF[\[Phi], (k)^2]- EllipticE[\[Phi], (k)^2])/ (k)^(2) |
Successful | Failure | - | Error |
| 19.2#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = \incellintFk@{\pi/2}{k}} | EllipticK(k)= EllipticF(sin(Pi/ 2), k) |
EllipticK[(k)^2]= EllipticF[Pi/ 2, (k)^2] |
Successful | Successful | - | - |
| 19.2#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{k} = \incellintEk@{\pi/2}{k}} | EllipticE(k)= EllipticE(sin(Pi/ 2), k) |
EllipticE[(k)^2]= EllipticE[Pi/ 2, (k)^2] |
Successful | Successful | - | - |
| 19.2#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintDk@{k} = \incellintDk@{\pi/2}{k}} | (EllipticK(k) - EllipticE(k))/(k)^2 = (EllipticF(sin(Pi/ 2), k) - EllipticE(sin(Pi/ 2), k))/(k)^2 |
Divide[EllipticK[(k)^2] - EllipticE[(k)^2], (k)^4]= Divide[EllipticF[Pi/ 2, (k)^2] - EllipticE[Pi/ 2, (k)^2], (k)^4] |
Successful | Successful | - | - |
| 19.2#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintDk@{\pi/2}{k} = (\compellintKk@{k}-\compellintEk@{k})/k^{2}} | (EllipticF(sin(Pi/ 2), k) - EllipticE(sin(Pi/ 2), k))/(k)^2 =(EllipticK(k)- EllipticE(k))/ (k)^(2) |
Divide[EllipticF[Pi/ 2, (k)^2] - EllipticE[Pi/ 2, (k)^2], (k)^4]=(EllipticK[(k)^2]- EllipticE[(k)^2])/ (k)^(2) |
Successful | Failure | - | Fail
Complex[-0.08185805455243832, 0.4541460103381725] <- {Rule[k, 2]}Complex[-0.027015555974087394, 0.3299973634705001] <- {Rule[k, 3]} |
| 19.2#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintPik@{\alpha^{2}}{k} = \incellintPik@{\pi/2}{\alpha^{2}}{k}} | EllipticPi((alpha)^(2), k)= EllipticPi(sin(Pi/ 2), (alpha)^(2), k) |
EllipticPi[(\[Alpha])^(2), (k)^2]= EllipticPi[(\[Alpha])^(2), Pi/ 2,(k)^2] |
Successful | Successful | - | - |
| 19.2#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{m\pi+\phi}{k} = 2m\compellintKk@{k}+\incellintFk@{\phi}{k}} | EllipticF(sin(m*Pi + phi), k)= 2*m*EllipticK(k)+ EllipticF(sin(phi), k) |
EllipticF[m*Pi + \[Phi], (k)^2]= 2*m*EllipticK[(k)^2]+ EllipticF[\[Phi], (k)^2] |
Failure | Failure | Error | Successful |
| 19.2#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{m\pi-\phi}{k} = 2m\compellintKk@{k}-\incellintFk@{\phi}{k}} | EllipticF(sin(m*Pi - phi), k)= 2*m*EllipticK(k)- EllipticF(sin(phi), k) |
EllipticF[m*Pi - \[Phi], (k)^2]= 2*m*EllipticK[(k)^2]- EllipticF[\[Phi], (k)^2] |
Failure | Failure | Error | Successful |
| 19.2#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{m\pi+\phi}{k} = 2m\compellintEk@{k}+\incellintEk@{\phi}{k}} | EllipticE(sin(m*Pi + phi), k)= 2*m*EllipticE(k)+ EllipticE(sin(phi), k) |
EllipticE[m*Pi + \[Phi], (k)^2]= 2*m*EllipticE[(k)^2]+ EllipticE[\[Phi], (k)^2] |
Failure | Failure | Fail -6.303071081-.6035229402*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, m = 1}-3.999999999-.16e-8*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, m = 2}-10.30307108-.6035229462*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, m = 3}-8.695154357-1.322364992*I <- {phi = 2^(1/2)+I*2^(1/2), k = 2, m = 1}... skip entries to safe data |
Successful |
| 19.2#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{m\pi-\phi}{k} = 2m\compellintEk@{k}-\incellintEk@{\phi}{k}} | EllipticE(sin(m*Pi - phi), k)= 2*m*EllipticE(k)- EllipticE(sin(phi), k) |
EllipticE[m*Pi - \[Phi], (k)^2]= 2*m*EllipticE[(k)^2]- EllipticE[\[Phi], (k)^2] |
Failure | Failure | Fail 2.303071080+.6035229417*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, m = 1}-4.000000000-.15e-8*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, m = 2}-1.696928920+.6035229433*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, m = 3}7.069958809-4.053051928*I <- {phi = 2^(1/2)+I*2^(1/2), k = 2, m = 1}... skip entries to safe data |
Successful |
| 19.2#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintDk@{m\pi+\phi}{k} = 2m\compellintDk@{k}+\incellintDk@{\phi}{k}} | (EllipticF(sin(m*Pi + phi), k) - EllipticE(sin(m*Pi + phi), k))/(k)^2 = 2*m*(EllipticK(k) - EllipticE(k))/(k)^2 + (EllipticF(sin(phi), k) - EllipticE(sin(phi), k))/(k)^2 |
Divide[EllipticF[m*Pi + \[Phi], (k)^2] - EllipticE[m*Pi + \[Phi], (k)^2], (k)^4]= 2*m*Divide[EllipticK[(k)^2] - EllipticE[(k)^2], (k)^4]+ Divide[EllipticF[\[Phi], (k)^2] - EllipticE[\[Phi], (k)^2], (k)^4] |
Failure | Failure | Error | Successful |
| 19.2#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintDk@{m\pi-\phi}{k} = 2m\compellintDk@{k}-\incellintDk@{\phi}{k}} | (EllipticF(sin(m*Pi - phi), k) - EllipticE(sin(m*Pi - phi), k))/(k)^2 = 2*m*(EllipticK(k) - EllipticE(k))/(k)^2 - (EllipticF(sin(phi), k) - EllipticE(sin(phi), k))/(k)^2 |
Divide[EllipticF[m*Pi - \[Phi], (k)^2] - EllipticE[m*Pi - \[Phi], (k)^2], (k)^4]= 2*m*Divide[EllipticK[(k)^2] - EllipticE[(k)^2], (k)^4]- Divide[EllipticF[\[Phi], (k)^2] - EllipticE[\[Phi], (k)^2], (k)^4] |
Failure | Failure | Error | Successful |
| 19.2#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = \tan@@{\phi}} | x = tan(phi) |
x = Tan[\[Phi]] |
Failure | Failure | Fail .9591286913-1.118374137*I <- {phi = 2^(1/2)+I*2^(1/2), x = 1}1.959128691-1.118374137*I <- {phi = 2^(1/2)+I*2^(1/2), x = 2}2.959128691-1.118374137*I <- {phi = 2^(1/2)+I*2^(1/2), x = 3}.9591286913+1.118374137*I <- {phi = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[0.9591286914366802, -1.1183741374008342] <- {Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.9591286914366801, -1.1183741374008342] <- {Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.95912869143668, -1.1183741374008342] <- {Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.9591286914366802, 1.1183741374008342] <- {Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.4#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{\compellintKk@{k}}{k} = \frac{\compellintEk@{k}-{k^{\prime}}^{2}\compellintKk@{k}}{k{k^{\prime}}^{2}}} | diff(EllipticK(k), k)=(EllipticE(k)- 1 - (k)^(2)* EllipticK(k))/(k*1 - (k)^(2)) |
D[EllipticK[(k)^2], k]=Divide[EllipticE[(k)^2]- 1 - (k)^(2)* EllipticK[(k)^2],k*1 - (k)^(2)] |
Failure | Failure | Error | Fail
Complex[-2.4717549813624253, 3.1435959698369205] <- {Rule[k, 2]}Complex[-1.12187012081601, 1.8575646745447774] <- {Rule[k, 3]} |
| 19.4#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{(\compellintEk@{k}-{k^{\prime}}^{2}\compellintKk@{k})}{k} = k\compellintKk@{k}} | diff(EllipticE(k)- 1 - (k)^(2)* EllipticK(k), k)= k*EllipticK(k) |
D[EllipticE[(k)^2]- 1 - (k)^(2)* EllipticK[(k)^2], k]= k*EllipticK[(k)^2] |
Failure | Failure | Error | Fail
Complex[-3.3189229307917216, 6.419990143492479] <- {Rule[k, 2]}Complex[-3.226352319798031, 7.107872714050419] <- {Rule[k, 3]} |
| 19.4#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{\compellintEk@{k}}{k} = \frac{\compellintEk@{k}-\compellintKk@{k}}{k}} | diff(EllipticE(k), k)=(EllipticE(k)- EllipticK(k))/(k) |
D[EllipticE[(k)^2], k]=Divide[EllipticE[(k)^2]- EllipticK[(k)^2],k] |
Successful | Successful | - | - |
| 19.4#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{(\compellintEk@{k}-\compellintKk@{k})}{k} = -\frac{k\compellintEk@{k}}{{k^{\prime}}^{2}}} | diff(EllipticE(k)- EllipticK(k), k)= -(k*EllipticE(k))/(1 - (k)^(2)) |
D[EllipticE[(k)^2]- EllipticK[(k)^2], k]= -Divide[k*EllipticE[(k)^2],1 - (k)^(2)] |
Successful | Successful | - | - |
| 19.4.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{\compellintEk@{k}}{k} = -\frac{1}{k}\deriv{\compellintKk@{k}}{k}} | diff(EllipticE(k), [k$(2)])= -(1)/(k)*diff(EllipticK(k), k) |
D[EllipticE[(k)^2], {k, 2}]= -Divide[1,k]*D[EllipticK[(k)^2], k] |
Successful | Successful | - | - |
| 19.4.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\frac{1}{k}\deriv{\compellintKk@{k}}{k} = \frac{{k^{\prime}}^{2}\compellintKk@{k}-\compellintEk@{k}}{k^{2}{k^{\prime}}^{2}}} | -(1)/(k)*diff(EllipticK(k), k)=(1 - (k)^(2)* EllipticK(k)- EllipticE(k))/((k)^(2)* 1 - (k)^(2)) |
-Divide[1,k]*D[EllipticK[(k)^2], k]=Divide[1 - (k)^(2)* EllipticK[(k)^2]- EllipticE[(k)^2],(k)^(2)* 1 - (k)^(2)] |
Error | Failure | - | Fail
|
| 19.4.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\compellintPik@{\alpha^{2}}{k}}{k} = \frac{k}{{k^{\prime}}^{2}(k^{2}-\alpha^{2})}(\compellintEk@{k}-{k^{\prime}}^{2}\compellintPik@{\alpha^{2}}{k})} | diff(EllipticPi((alpha)^(2), k), k)=(k)/(1 - (k)^(2)*((k)^(2)- (alpha)^(2)))*(EllipticE(k)- 1 - (k)^(2)* EllipticPi((alpha)^(2), k)) |
D[EllipticPi[(\[Alpha])^(2), (k)^2], k]=Divide[k,1 - (k)^(2)*((k)^(2)- (\[Alpha])^(2))]*(EllipticE[(k)^2]- 1 - (k)^(2)* EllipticPi[(\[Alpha])^(2), (k)^2]) |
Failure | Failure | Error | Fail
Complex[-0.5687202790618282, -0.6586049032127743] <- {Rule[k, 2], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.5507473882918545, -0.09813531953107986] <- {Rule[k, 3], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.06853665940289096, 0.43401271964497673] <- {Rule[k, 2], Rule[α, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.022201879042164176, 0.3037111242639709] <- {Rule[k, 3], Rule[α, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.4.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\incellintFk@{\phi}{k}}{k} = {\frac{\incellintEk@{\phi}{k}-{k^{\prime}}^{2}\incellintFk@{\phi}{k}}{k{k^{\prime}}^{2}}-\frac{k\sin@@{\phi}\cos@@{\phi}}{{k^{\prime}}^{2}\sqrt{1-k^{2}\sin^{2}@@{\phi}}}}} | diff(EllipticF(sin(phi), k), k)=(EllipticE(sin(phi), k)- 1 - (k)^(2)* EllipticF(sin(phi), k))/(k*1 - (k)^(2))-(k*sin(phi)*cos(phi))/(1 - (k)^(2)*sqrt(1 - (k)^(2)* (sin(phi))^(2))) |
D[EllipticF[\[Phi], (k)^2], k]=Divide[EllipticE[\[Phi], (k)^2]- 1 - (k)^(2)* EllipticF[\[Phi], (k)^2],k*1 - (k)^(2)]-Divide[k*Sin[\[Phi]]*Cos[\[Phi]],1 - (k)^(2)*Sqrt[1 - (k)^(2)* (Sin[\[Phi]])^(2)]] |
Failure | Failure | Fail Float(infinity)+Float(infinity)*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1}.3848531746-2.832892174*I <- {phi = 2^(1/2)+I*2^(1/2), k = 2}.2974950167-1.686437583*I <- {phi = 2^(1/2)+I*2^(1/2), k = 3}Float(infinity)+Float(infinity)*I <- {phi = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[0.3848531762144859, -2.8328921744194435] <- {Rule[k, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.297495017249507, -1.6864375827943054] <- {Rule[k, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.38485317621448545, 2.8328921744194426] <- {Rule[k, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.2974950172495072, 1.686437582794305] <- {Rule[k, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.4.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\incellintEk@{\phi}{k}}{k} = \frac{\incellintEk@{\phi}{k}-\incellintFk@{\phi}{k}}{k}} | diff(EllipticE(sin(phi), k), k)=(EllipticE(sin(phi), k)- EllipticF(sin(phi), k))/(k) |
D[EllipticE[\[Phi], (k)^2], k]=Divide[EllipticE[\[Phi], (k)^2]- EllipticF[\[Phi], (k)^2],k] |
Successful | Successful | - | - |
| 19.4.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\incellintPik@{\phi}{\alpha^{2}}{k}}{k} = \frac{k}{{k^{\prime}}^{2}(k^{2}-\alpha^{2})}\left({\incellintEk@{\phi}{k}-{k^{\prime}}^{2}\incellintPik@{\phi}{\alpha^{2}}{k}}-\frac{k^{2}\sin@@{\phi}\cos@@{\phi}}{\sqrt{1-k^{2}\sin^{2}@@{\phi}}}\right)} | diff(EllipticPi(sin(phi), (alpha)^(2), k), k)=(k)/(1 - (k)^(2)*((k)^(2)- (alpha)^(2)))*(EllipticE(sin(phi), k)- 1 - (k)^(2)* EllipticPi(sin(phi), (alpha)^(2), k)-((k)^(2)* sin(phi)*cos(phi))/(sqrt(1 - (k)^(2)* (sin(phi))^(2)))) |
D[EllipticPi[(\[Alpha])^(2), \[Phi],(k)^2], k]=Divide[k,1 - (k)^(2)*((k)^(2)- (\[Alpha])^(2))]*(EllipticE[\[Phi], (k)^2]- 1 - (k)^(2)* EllipticPi[(\[Alpha])^(2), \[Phi],(k)^2]-Divide[(k)^(2)* Sin[\[Phi]]*Cos[\[Phi]],Sqrt[1 - (k)^(2)* (Sin[\[Phi]])^(2)]]) |
Failure | Failure | Fail Float(undefined)+Float(undefined)*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k = 1}.3340407480e-1-.3675640793*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k = 2}-.3093953717e-1-.2652186316*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k = 3}Float(undefined)+Float(undefined)*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[0.0334040747326544, -0.36756407921347006] <- {Rule[k, 2], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.030939537020799865, -0.265218631561315] <- {Rule[k, 3], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.15465722767175843, 0.23001025865583416] <- {Rule[k, 2], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.030260984981937494, 0.2341460018375755] <- {Rule[k, 3], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (k{k^{\prime}}^{2}D_{k}^{2}+(1-3k^{2})D_{k}-k)\incellintFk@{\phi}{k} = \frac{-k\sin@@{\phi}\cos@@{\phi}}{(1-k^{2}\sin^{2}@@{\phi})^{3/2}}} | (k*1 - (k)^(2)* D(D[k])^(2)+(1 - 3*(k)^(2))*D[k]- k)* EllipticF(sin(phi), k)=(- k*sin(phi)*cos(phi))/((1 - (k)^(2)* (sin(phi))^(2))^(3/ 2)) |
(k*1 - (k)^(2)* D(Subscript[D, k])^(2)+(1 - 3*(k)^(2))*Subscript[D, k]- k)* EllipticF[\[Phi], (k)^2]=Divide[- k*Sin[\[Phi]]*Cos[\[Phi]],(1 - (k)^(2)* (Sin[\[Phi]])^(2))^(3/ 2)] |
Error | Failure | - | Successful |
| 19.4.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (k{k^{\prime}}^{2}D_{k}^{2}+{k^{\prime}}^{2}D_{k}+k)\incellintEk@{\phi}{k} = \frac{k\sin@@{\phi}\cos@@{\phi}}{\sqrt{1-k^{2}\sin^{2}@@{\phi}}}} | (k*1 - (k)^(2)* D(D[k])^(2)+ 1 - (k)^(2)* D[k]+ k)* EllipticE(sin(phi), k)=(k*sin(phi)*cos(phi))/(sqrt(1 - (k)^(2)* (sin(phi))^(2))) |
(k*1 - (k)^(2)* D(Subscript[D, k])^(2)+ 1 - (k)^(2)* Subscript[D, k]+ k)* EllipticE[\[Phi], (k)^2]=Divide[k*Sin[\[Phi]]*Cos[\[Phi]],Sqrt[1 - (k)^(2)* (Sin[\[Phi]])^(2)]] |
Error | Failure | - | Successful |
| 19.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = \frac{\pi}{2}\sum_{m=0}^{\infty}\frac{\Pochhammersym{\tfrac{1}{2}}{m}\Pochhammersym{\tfrac{1}{2}}{m}}{m!\;m!}k^{2m}} | EllipticK(k)=(Pi)/(2)*sum((pochhammer((1)/(2), m)*pochhammer((1)/(2), m))/(factorial(m)*factorial(m))*(k)^(2*m), m = 0..infinity) |
EllipticK[(k)^2]=Divide[Pi,2]*Sum[Divide[Pochhammer[Divide[1,2], m]*Pochhammer[Divide[1,2], m],(m)!*(m)!]*(k)^(2*m), {m, 0, Infinity}] |
Failure | Successful | Skip | - |
| 19.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\pi}{2}\sum_{m=0}^{\infty}\frac{\Pochhammersym{\tfrac{1}{2}}{m}\Pochhammersym{\tfrac{1}{2}}{m}}{m!\;m!}k^{2m} = \frac{\pi}{2}\genhyperF{2}{1}@{\tfrac{1}{2},\tfrac{1}{2}}{1}{k^{2}}} | (Pi)/(2)*sum((pochhammer((1)/(2), m)*pochhammer((1)/(2), m))/(factorial(m)*factorial(m))*(k)^(2*m), m = 0..infinity)=(Pi)/(2)*hypergeom([(1)/(2),(1)/(2)], [1], (k)^(2)) |
Divide[Pi,2]*Sum[Divide[Pochhammer[Divide[1,2], m]*Pochhammer[Divide[1,2], m],(m)!*(m)!]*(k)^(2*m), {m, 0, Infinity}]=Divide[Pi,2]*HypergeometricPFQ[{Divide[1,2],Divide[1,2]}, {1}, (k)^(2)] |
Failure | Successful | Skip | - |
| 19.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{k} = \frac{\pi}{2}\sum_{m=0}^{\infty}\frac{\Pochhammersym{-\tfrac{1}{2}}{m}\Pochhammersym{\tfrac{1}{2}}{m}}{m!\;m!}k^{2m}} | EllipticE(k)=(Pi)/(2)*sum((pochhammer(-(1)/(2), m)*pochhammer((1)/(2), m))/(factorial(m)*factorial(m))*(k)^(2*m), m = 0..infinity) |
EllipticE[(k)^2]=Divide[Pi,2]*Sum[Divide[Pochhammer[-Divide[1,2], m]*Pochhammer[Divide[1,2], m],(m)!*(m)!]*(k)^(2*m), {m, 0, Infinity}] |
Failure | Successful | Skip | - |
| 19.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\pi}{2}\sum_{m=0}^{\infty}\frac{\Pochhammersym{-\tfrac{1}{2}}{m}\Pochhammersym{\tfrac{1}{2}}{m}}{m!\;m!}k^{2m} = \frac{\pi}{2}\genhyperF{2}{1}@{-\tfrac{1}{2},\tfrac{1}{2}}{1}{k^{2}}} | (Pi)/(2)*sum((pochhammer(-(1)/(2), m)*pochhammer((1)/(2), m))/(factorial(m)*factorial(m))*(k)^(2*m), m = 0..infinity)=(Pi)/(2)*hypergeom([-(1)/(2),(1)/(2)], [1], (k)^(2)) |
Divide[Pi,2]*Sum[Divide[Pochhammer[-Divide[1,2], m]*Pochhammer[Divide[1,2], m],(m)!*(m)!]*(k)^(2*m), {m, 0, Infinity}]=Divide[Pi,2]*HypergeometricPFQ[{-Divide[1,2],Divide[1,2]}, {1}, (k)^(2)] |
Failure | Successful | Skip | - |
| 19.5.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintDk@{k} = \frac{\pi}{4}\sum_{m=0}^{\infty}\frac{\Pochhammersym{\tfrac{3}{2}}{m}\Pochhammersym{\tfrac{1}{2}}{m}}{(m+1)!\;m!}k^{2m}} | (EllipticK(k) - EllipticE(k))/(k)^2 =(Pi)/(4)*sum((pochhammer((3)/(2), m)*pochhammer((1)/(2), m))/(factorial(m + 1)*factorial(m))*(k)^(2*m), m = 0..infinity) |
Divide[EllipticK[(k)^2] - EllipticE[(k)^2], (k)^4]=Divide[Pi,4]*Sum[Divide[Pochhammer[Divide[3,2], m]*Pochhammer[Divide[1,2], m],(m + 1)!*(m)!]*(k)^(2*m), {m, 0, Infinity}] |
Failure | Failure | Skip | Fail
Complex[-0.08185805455243848, 0.4541460103381727] <- {Rule[k, 2]}Complex[-0.02701555597408747, 0.3299973634705002] <- {Rule[k, 3]} |
| 19.5.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\pi}{4}\sum_{m=0}^{\infty}\frac{\Pochhammersym{\tfrac{3}{2}}{m}\Pochhammersym{\tfrac{1}{2}}{m}}{(m+1)!\;m!}k^{2m} = \frac{\pi}{4}\genhyperF{2}{1}@{\tfrac{3}{2},\tfrac{1}{2}}{2}{k^{2}}} | (Pi)/(4)*sum((pochhammer((3)/(2), m)*pochhammer((1)/(2), m))/(factorial(m + 1)*factorial(m))*(k)^(2*m), m = 0..infinity)=(Pi)/(4)*hypergeom([(3)/(2),(1)/(2)], [2], (k)^(2)) |
Divide[Pi,4]*Sum[Divide[Pochhammer[Divide[3,2], m]*Pochhammer[Divide[1,2], m],(m + 1)!*(m)!]*(k)^(2*m), {m, 0, Infinity}]=Divide[Pi,4]*HypergeometricPFQ[{Divide[3,2],Divide[1,2]}, {2}, (k)^(2)] |
Failure | Successful | Skip | - |
| 19.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q = \exp@{-\pi\ccompellintKk@{k}/\compellintKk@{k}}} | q = exp(- Pi*EllipticCK(k)/ EllipticK(k)) |
q = Exp[- Pi*EllipticK[1-(k)^2]/ EllipticK[(k)^2]] |
Failure | Failure | Skip | Fail
Complex[0.41421356237309515, 1.4142135623730951] <- {Rule[k, 1], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.41421356237309515, -1.4142135623730951] <- {Rule[k, 1], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.414213562373095, -1.4142135623730951] <- {Rule[k, 1], Rule[q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.414213562373095, 1.4142135623730951] <- {Rule[k, 1], Rule[q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 19.5.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = \frac{\pi}{2}\left(1+2\sum_{n=1}^{\infty}q^{n^{2}}\right)^{2}} | EllipticK(k)=(Pi)/(2)*(1 + 2*sum((q)^((n)^(2)), n = 1..infinity))^(2) |
EllipticK[(k)^2]=Divide[Pi,2]*(1 + 2*Sum[(q)^((n)^(2)), {n, 1, Infinity}])^(2) |
Failure | Failure | Skip | Fail
DirectedInfinity[] <- {Rule[k, 1], Rule[q, Rational[1, 2]]}Complex[-6.276558134259685, -1.0782578237498217] <- {Rule[k, 2], Rule[q, Rational[1, 2]]}Complex[-6.580304399791072, -0.842875177406298] <- {Rule[k, 3], Rule[q, Rational[1, 2]]} |
| 19.5.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{k} = \compellintKk@{k}+\frac{2\pi^{2}}{\compellintKk@{k}}\,\frac{\sum_{n=1}^{\infty}(-1)^{n}n^{2}q^{n^{2}}}{1+2\sum_{n=1}^{\infty}(-1)^{n}q^{n^{2}}}} | EllipticE(k)= EllipticK(k)+(2*(Pi)^(2))/(EllipticK(k))*(sum((- 1)^(n)* (n)^(2)* (q)^((n)^(2)), n = 1..infinity))/(1 + 2*sum((- 1)^(n)* (q)^((n)^(2)), n = 1..infinity)) |
EllipticE[(k)^2]= EllipticK[(k)^2]+Divide[2*(Pi)^(2),EllipticK[(k)^2]]*Divide[Sum[(- 1)^(n)* (n)^(2)* (q)^((n)^(2)), {n, 1, Infinity}],1 + 2*Sum[(- 1)^(n)* (q)^((n)^(2)), {n, 1, Infinity}]] |
Failure | Failure | Skip | Error |
| 19.5.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = \frac{\pi}{2}\prod_{m=1}^{\infty}(1+k_{m})} | EllipticK(k)=(Pi)/(2)*product(1 + k[m], m = 1..infinity) |
EllipticK[(k)^2]=Divide[Pi,2]*Product[1 + Subscript[k, m], {m, 1, Infinity}] |
Failure | Failure | Skip | Skip |
| 19.6#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{0} = \compellintEk@{0}} | EllipticK(0)= EllipticE(0) |
EllipticK[(0)^2]= EllipticE[(0)^2] |
Successful | Successful | - | - |
| 19.6#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{0} = \ccompellintKk@{1}} | EllipticE(0)= EllipticCK(1) |
EllipticE[(0)^2]= EllipticK[1-(1)^2] |
Successful | Successful | - | - |
| 19.6#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ccompellintKk@{1} = \ccompellintEk@{1}} | EllipticCK(1)= EllipticCE(1) |
EllipticK[1-(1)^2]= EllipticE[1-(1)^2] |
Successful | Successful | - | - |
| 19.6#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ccompellintEk@{1} = \tfrac{1}{2}\pi} | EllipticCE(1)=(1)/(2)*Pi |
EllipticE[1-(1)^2]=Divide[1,2]*Pi |
Successful | Successful | - | - |
| 19.6#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{1} = \ccompellintKk@{0}} | EllipticK(1)= EllipticCK(0) |
EllipticK[(1)^2]= EllipticK[1-(0)^2] |
Error | Failure | - | Fail
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[Indeterminate, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[Indeterminate, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[Indeterminate, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[Indeterminate, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 19.6#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ccompellintKk@{0} = \infty} | EllipticCK(0)= infinity |
EllipticK[1-(0)^2]= Infinity |
Error | Failure | - | Fail
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[Indeterminate, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[Indeterminate, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[Indeterminate, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[Indeterminate, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 19.6#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{1} = \ccompellintEk@{0}} | EllipticE(1)= EllipticCE(0) |
EllipticE[(1)^2]= EllipticE[1-(0)^2] |
Successful | Successful | - | - |
| 19.6#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ccompellintEk@{0} = 1} | EllipticCE(0)= 1 |
EllipticE[1-(0)^2]= 1 |
Successful | Successful | - | - |
| 19.6#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintPik@{k^{2}}{k} = \compellintEk@{k}/{k^{\prime}}^{2}} | EllipticPi((k)^(2), k)= EllipticE(k)/ 1 - (k)^(2) |
EllipticPi[(k)^(2), (k)^2]= EllipticE[(k)^2]/ 1 - (k)^(2) |
Failure | Failure | Fail Float(infinity) <- {k = 1}3.458268152-1.791805641*I <- {k = 2}8.701204041-2.810641644*I <- {k = 3} |
Fail
DirectedInfinity[] <- {Rule[k, 1]}Complex[3.4582681513867195, -1.791805641849464] <- {Rule[k, 2]}Complex[8.701204041408065, -2.8106416436990806] <- {Rule[k, 3]} |
| 19.6#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintPik@{-k}{k} = \tfrac{1}{4}\pi(1+k)^{-1}+\tfrac{1}{2}\compellintKk@{k}} | EllipticPi(- k, k)=(1)/(4)*Pi*(1 + k)^(- 1)+(1)/(2)*EllipticK(k) |
EllipticPi[- k, (k)^2]=Divide[1,4]*Pi*(1 + k)^(- 1)+Divide[1,2]*EllipticK[(k)^2] |
Failure | Failure | Error | Successful |
| 19.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintPik@{\alpha^{2}}{0} = \pi/(2\sqrt{1-\alpha^{2}}),\quad\compellintPik@{0}{k}} | EllipticPi((alpha)^(2), 0)= Pi/(2*sqrt(1 - (alpha)^(2))), EllipticPi(0, k) |
EllipticPi[(\[Alpha])^(2), (0)^2]= Pi/(2*Sqrt[1 - (\[Alpha])^(2)]), EllipticPi[0, (k)^2] |
Error | Failure | - | Error |
| 19.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pi/(2\sqrt{1-\alpha^{2}}),\quad\compellintPik@{0}{k} = \compellintKk@{k}} | Pi/(2*sqrt(1 - (alpha)^(2))), EllipticPi(0, k)= EllipticK(k) |
Pi/(2*Sqrt[1 - (\[Alpha])^(2)]), EllipticPi[0, (k)^2]= EllipticK[(k)^2] |
Error | Failure | - | Error |
| 19.6.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintPik@{\alpha^{2}}{k} = \compellintKk@{k}-\compellintPik@{k^{2}/\alpha^{2}}{k}} | EllipticPi((alpha)^(2), k)= EllipticK(k)- EllipticPi((k)^(2)/ (alpha)^(2), k) |
EllipticPi[(\[Alpha])^(2), (k)^2]= EllipticK[(k)^2]- EllipticPi[(k)^(2)/ (\[Alpha])^(2), (k)^2] |
Failure | Failure | Error | Fail
Complex[0.6269006702249605, 0.17364143326773873] <- {Rule[k, 2], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.4911490398753759, 0.04265145338289439] <- {Rule[k, 3], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.6269006702249589, -0.17364143326773473] <- {Rule[k, 2], Rule[α, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.49114903987537695, -0.042651453382894666] <- {Rule[k, 3], Rule[α, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.6#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintPik@{\alpha^{2}}{0} = 0} | EllipticPi((alpha)^(2), 0)= 0 |
EllipticPi[(\[Alpha])^(2), (0)^2]= 0 |
Failure | Failure | Fail .6097433517+.4760732230*I <- {alpha = 2^(1/2)+I*2^(1/2)}.6097433517-.4760732230*I <- {alpha = 2^(1/2)-I*2^(1/2)}.6097433517+.4760732230*I <- {alpha = -2^(1/2)-I*2^(1/2)}.6097433517-.4760732230*I <- {alpha = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.6097433514448427, 0.4760732227700887] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.6097433514448427, -0.4760732227700887] <- {Rule[α, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.6097433514448427, 0.4760732227700887] <- {Rule[α, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.6097433514448427, -0.4760732227700887] <- {Rule[α, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 19.6#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{0}{k} = 0} | EllipticF(sin(0), k)= 0 |
EllipticF[0, (k)^2]= 0 |
Successful | Successful | - | - |
| 19.6#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{0} = \phi} | EllipticF(sin(phi), 0)= phi |
EllipticF[\[Phi], (0)^2]= \[Phi] |
Failure | Successful | Successful | - |
| 19.6#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\tfrac{1}{2}\pi}{1} = \infty} | EllipticF(sin((1)/(2)*Pi), 1)= infinity |
EllipticF[Divide[1,2]*Pi, (1)^2]= Infinity |
Error | Failure | - | Fail
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[Indeterminate, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[Indeterminate, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[Indeterminate, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[Indeterminate, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 19.6#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\tfrac{1}{2}\pi}{k} = \compellintKk@{k}} | EllipticF(sin((1)/(2)*Pi), k)= EllipticK(k) |
EllipticF[Divide[1,2]*Pi, (k)^2]= EllipticK[(k)^2] |
Successful | Successful | - | - |
| 19.6#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{\phi\to 0}\ifrac{\incellintFk@{\phi}{k}}{\phi} = 1} | limit((EllipticF(sin(phi), k))/(phi), phi = 0)= 1 |
Limit[Divide[EllipticF[\[Phi], (k)^2],\[Phi]], \[Phi] -> 0]= 1 |
Successful | Successful | - | - |
| 19.6#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{0}{k} = 0} | EllipticE(sin(0), k)= 0 |
EllipticE[0, (k)^2]= 0 |
Successful | Successful | - | - |
| 19.6#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{0} = \phi} | EllipticE(sin(phi), 0)= phi |
EllipticE[\[Phi], (0)^2]= \[Phi] |
Failure | Successful | Successful | - |
| 19.6#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\tfrac{1}{2}\pi}{1} = 1} | EllipticE(sin((1)/(2)*Pi), 1)= 1 |
EllipticE[Divide[1,2]*Pi, (1)^2]= 1 |
Successful | Successful | - | - |
| 19.6#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{1} = \sin@@{\phi}} | EllipticE(sin(phi), 1)= sin(phi) |
EllipticE[\[Phi], (1)^2]= Sin[\[Phi]] |
Successful | Failure | - | Successful |
| 19.6#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\tfrac{1}{2}\pi}{k} = \compellintEk@{k}} | EllipticE(sin((1)/(2)*Pi), k)= EllipticE(k) |
EllipticE[Divide[1,2]*Pi, (k)^2]= EllipticE[(k)^2] |
Successful | Successful | - | - |
| 19.6.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{\phi\to 0}\ifrac{\incellintEk@{\phi}{k}}{\phi} = 1} | limit((EllipticE(sin(phi), k))/(phi), phi = 0)= 1 |
Limit[Divide[EllipticE[\[Phi], (k)^2],\[Phi]], \[Phi] -> 0]= 1 |
Successful | Successful | - | - |
| 19.6#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{0}{\alpha^{2}}{k} = 0} | EllipticPi(sin(0), (alpha)^(2), k)= 0 |
EllipticPi[(\[Alpha])^(2), 0,(k)^2]= 0 |
Successful | Successful | - | - |
| 19.6#Ex22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{0}{0} = \phi} | EllipticPi(sin(phi), 0, 0)= phi |
EllipticPi[0, \[Phi],(0)^2]= \[Phi] |
Failure | Successful | Successful | - |
| 19.6#Ex23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{1}{0} = \tan@@{\phi}} | EllipticPi(sin(phi), 1, 0)= tan(phi) |
EllipticPi[1, \[Phi],(0)^2]= Tan[\[Phi]] |
Failure | Successful | Successful | - |
| 19.6#Ex27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{0}{k} = \incellintFk@{\phi}{k}} | EllipticPi(sin(phi), 0, k)= EllipticF(sin(phi), k) |
EllipticPi[0, \[Phi],(k)^2]= EllipticF[\[Phi], (k)^2] |
Successful | Successful | - | - |
| 19.6#Ex28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{k^{2}}{k} = \frac{1}{{k^{\prime}}^{2}}\left(\incellintEk@{\phi}{k}-\frac{k^{2}}{\Delta}\sin@@{\phi}\cos@@{\phi}\right)} | EllipticPi(sin(phi), (k)^(2), k)=(1)/(1 - (k)^(2))*(EllipticE(sin(phi), k)-((k)^(2))/(Delta)*sin(phi)*cos(phi)) |
EllipticPi[(k)^(2), \[Phi],(k)^2]=Divide[1,1 - (k)^(2)]*(EllipticE[\[Phi], (k)^2]-Divide[(k)^(2),\[CapitalDelta]]*Sin[\[Phi]]*Cos[\[Phi]]) |
Failure | Failure | Fail Float(infinity)+Float(infinity)*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k = 1}2.583555547+2.729095606*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k = 2}1.800281293+2.241476784*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k = 3}Float(infinity)+Float(infinity)*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[2.5835555495392164, 2.729095607128086] <- {Rule[k, 2], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.8002812942897588, 2.24147678315869] <- {Rule[k, 3], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.1970424154535648, -1.4962733566009967] <- {Rule[k, 2], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.3895982386729004, -1.2012830092764584] <- {Rule[k, 3], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.6#Ex29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{1}{k} = \incellintFk@{\phi}{k}-\frac{1}{{k^{\prime}}^{2}}(\incellintEk@{\phi}{k}-\Delta\tan@@{\phi})} | EllipticPi(sin(phi), 1, k)= EllipticF(sin(phi), k)-(1)/(1 - (k)^(2))*(EllipticE(sin(phi), k)- Delta*tan(phi)) |
EllipticPi[1, \[Phi],(k)^2]= EllipticF[\[Phi], (k)^2]-Divide[1,1 - (k)^(2)]*(EllipticE[\[Phi], (k)^2]- \[CapitalDelta]*Tan[\[Phi]]) |
Failure | Failure | Fail Float(infinity)+Float(infinity)*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k = 1}-2.077524150+.3723387150*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k = 2}-1.086812375+.1094418732*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k = 3}Float(infinity)+Float(infinity)*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-2.0775241504865902, 0.37233871531005636] <- {Rule[k, 2], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.0868123753385022, 0.1094418733619304] <- {Rule[k, 3], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.0231109018735427, -0.3338048760552679] <- {Rule[k, 2], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.6914074071086094, -0.09499168364138477] <- {Rule[k, 3], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.6#Ex30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\tfrac{1}{2}\pi}{\alpha^{2}}{k} = \compellintPik@{\alpha^{2}}{k}} | EllipticPi(sin((1)/(2)*Pi), (alpha)^(2), k)= EllipticPi((alpha)^(2), k) |
EllipticPi[(\[Alpha])^(2), Divide[1,2]*Pi,(k)^2]= EllipticPi[(\[Alpha])^(2), (k)^2] |
Successful | Successful | - | - |
| 19.6#Ex31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{\phi\to 0}\ifrac{\incellintPik@{\phi}{\alpha^{2}}{k}}{\phi} = 1} | limit((EllipticPi(sin(phi), (alpha)^(2), k))/(phi), phi = 0)= 1 |
Limit[Divide[EllipticPi[(\[Alpha])^(2), \[Phi],(k)^2],\[Phi]], \[Phi] -> 0]= 1 |
Successful | Successful | - | - |
| 19.7.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{k}\ccompellintKk@{k}+\ccompellintEk@{k}\compellintKk@{k}-\compellintKk@{k}\ccompellintKk@{k} = \tfrac{1}{2}\pi} | EllipticE(k)*EllipticCK(k)+ EllipticCE(k)*EllipticK(k)- EllipticK(k)*EllipticCK(k)=(1)/(2)*Pi |
EllipticE[(k)^2]*EllipticK[1-(k)^2]+ EllipticE[1-(k)^2]*EllipticK[(k)^2]- EllipticK[(k)^2]*EllipticK[1-(k)^2]=Divide[1,2]*Pi |
Failure | Failure | Error | Successful |
| 19.7#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{ik/k^{\prime}} = k^{\prime}\compellintKk@{k}} | EllipticK(I*k/sqrt(1 - (k)^(2)))=sqrt(1 - (k)^(2))*EllipticK(k) |
EllipticK[(I*k/Sqrt[1 - (k)^(2)])^2]=Sqrt[1 - (k)^(2)]*EllipticK[(k)^2] |
Failure | Failure | Error | Fail
Complex[-2.220446049250313*^-16, -2.9198052634126777] <- {Rule[k, 2]}Complex[0.0, -3.0497736761637926] <- {Rule[k, 3]} |
| 19.7#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{ik/k^{\prime}} = (1/k^{\prime})\compellintEk@{k}} | EllipticE(I*k/sqrt(1 - (k)^(2)))=(1/sqrt(1 - (k)^(2)))* EllipticE(k) |
EllipticE[(I*k/Sqrt[1 - (k)^(2)])^2]=(1/Sqrt[1 - (k)^(2)])* EllipticE[(k)^2] |
Failure | Failure | Fail Float(infinity)+Float(infinity)*I <- {k = 1}.6e-9+.4691535424*I <- {k = 2}-.5e-9+.1878050212*I <- {k = 3} |
Fail
Complex[-5.551115123125783*^-16, 0.46915354293820644] <- {Rule[k, 2]}Complex[2.220446049250313*^-16, 0.18780502089910417] <- {Rule[k, 3]} |
| 19.7#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{k_{1}} = k\incellintFk@{\beta}{k}} | EllipticF(sin(phi), k[1])= k*EllipticF(sin(beta), k) |
EllipticF[\[Phi], (Subscript[k, 1])^2]= k*EllipticF[\[Beta], (k)^2] |
Failure | Failure | Fail .1478755578-.6820014149*I <- {beta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), k = 1}.1609634146-1.274502936*I <- {beta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), k = 2}.1632109318-1.647695481*I <- {beta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), k = 3}.8504514854-1.466163968*I <- {beta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Successful |
| 19.7#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k_{1}} = (\incellintEk@{\beta}{k}-{k^{\prime}}^{2}\incellintFk@{\beta}{k})/k} | EllipticE(sin(phi), k[1])=(EllipticE(sin(beta), k)- 1 - (k)^(2)* EllipticF(sin(beta), k))/ k |
EllipticE[\[Phi], (Subscript[k, 1])^2]=(EllipticE[\[Beta], (k)^2]- 1 - (k)^(2)* EllipticF[\[Beta], (k)^2])/ k |
Failure | Failure | Fail 3.373306475+3.452491889*I <- {beta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), k = 1}3.041115012+4.688090748*I <- {beta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), k = 2}2.905177117+5.217063396*I <- {beta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), k = 3}-1.662478744+4.734343989*I <- {beta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Successful |
| 19.7#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{\alpha^{2}}{k_{1}} = k\incellintPik@{\beta}{k^{2}\alpha^{2}}{k}} | EllipticPi(sin(phi), (alpha)^(2), k[1])= k*EllipticPi(sin(beta), (k)^(2)* (alpha)^(2), k) |
EllipticPi[(\[Alpha])^(2), \[Phi],(Subscript[k, 1])^2]= k*EllipticPi[(k)^(2)* (\[Alpha])^(2), \[Beta],(k)^2] |
Failure | Failure | Skip | Successful |
| 19.7#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{\theta} = \frac{\sqrt{1+k^{2}}\sin@@{\phi}}{\sqrt{1+k^{2}\sin^{2}@@{\phi}}}} | sin(theta)=(sqrt(1 + (k)^(2))*sin(phi))/(sqrt(1 + (k)^(2)* (sin(phi))^(2))) |
Sin[\[Theta]]=Divide[Sqrt[1 + (k)^(2)]*Sin[\[Phi]],Sqrt[1 + (k)^(2)* (Sin[\[Phi]])^(2)]] |
Failure | Failure | Fail .863648898+.2706006291*I <- {phi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 1}1.061002746+.2942020964*I <- {phi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 2}1.109187756+.2984612377*I <- {phi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 3}.863648898-.3329223119*I <- {phi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[0.86364889928252, 0.27060062852924793] <- {Rule[k, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0610027472814447, 0.29420209574283873] <- {Rule[k, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.1091877569768196, 0.2984612371222133] <- {Rule[k, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.86364889928252, 0.3329223112062738] <- {Rule[k, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.7#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{i\phi}{k} = i\incellintFk@{\psi}{k^{\prime}}} | EllipticF(sin(I*phi), k)= I*EllipticF(sin(psi), sqrt(1 - (k)^(2))) |
EllipticF[I*\[Phi], (k)^2]= I*EllipticF[\[Psi], (Sqrt[1 - (k)^(2)])^2] |
Failure | Failure | Fail .9251391454+.76168273e-1*I <- {phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), k = 1}.3353318864+.3237108e-2*I <- {phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), k = 2}.2150344377+.8523035e-3*I <- {phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), k = 3}-1.903287979+.76168273e-1*I <- {phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[0.9251391460853863, 0.0761682733812794] <- {Rule[k, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.33533188682392046, 0.0032371074313650716] <- {Rule[k, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.21503443789021323, 8.523034067818847*^-4] <- {Rule[k, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.9032879786608041, 0.0761682733812794] <- {Rule[k, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.7#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{i\phi}{k} = i\left(\incellintFk@{\psi}{k^{\prime}}-\incellintEk@{\psi}{k^{\prime}}+(\tan@@{\psi})\sqrt{1-{k^{\prime}}^{2}\sin^{2}@@{\psi}}\right)} | EllipticE(sin(I*phi), k)= I*(EllipticF(sin(psi), sqrt(1 - (k)^(2)))- EllipticE(sin(psi), sqrt(1 - (k)^(2)))+(tan(psi))*sqrt(1 - 1 - (k)^(2)* (sin(psi))^(2))) |
EllipticE[I*\[Phi], (k)^2]= I*(EllipticF[\[Psi], (Sqrt[1 - (k)^(2)])^2]- EllipticE[\[Psi], (Sqrt[1 - (k)^(2)])^2]+(Tan[\[Psi]])*Sqrt[1 - 1 - (k)^(2)* (Sin[\[Psi]])^(2)]) |
Failure | Failure | Fail -1.901989389-2.116793618*I <- {phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), k = 1}-6.480561985-4.744566218*I <- {phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), k = 2}-10.28790921-7.196969925*I <- {phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), k = 3}-2.401081691-2.116793618*I <- {phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-1.9019893907701486, -2.1167936214122864] <- {Rule[k, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-6.480561989871777, -4.744566223003809] <- {Rule[k, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-10.28790921849954, -7.196969931680352] <- {Rule[k, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.401081691908424, -2.1167936214122864] <- {Rule[k, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.7#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{i\phi}{\alpha^{2}}{k} = i\left(\incellintFk@{\psi}{k^{\prime}}-\alpha^{2}\incellintPik@{\psi}{1-\alpha^{2}}{k^{\prime}}\right)/{(1-\alpha^{2})}} | EllipticPi(sin(I*phi), (alpha)^(2), k)= I*(EllipticF(sin(psi), sqrt(1 - (k)^(2)))- (alpha)^(2)* EllipticPi(sin(psi), 1 - (alpha)^(2), sqrt(1 - (k)^(2))))/(1 - (alpha)^(2)) |
EllipticPi[(\[Alpha])^(2), I*\[Phi],(k)^2]= I*(EllipticF[\[Psi], (Sqrt[1 - (k)^(2)])^2]- (\[Alpha])^(2)* EllipticPi[1 - (\[Alpha])^(2), \[Psi],(Sqrt[1 - (k)^(2)])^2])/(1 - (\[Alpha])^(2)) |
Failure | Failure | Skip | Skip |
| 19.8.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\AGM@{a_{0}}{g_{0}}} = \frac{2}{\pi}\int_{0}^{\pi/2}\frac{\diff{\theta}}{\sqrt{a_{0}^{2}\cos^{2}@@{\theta}+g_{0}^{2}\sin^{2}@@{\theta}}}} | (1)/(GaussAGM(a[0], g[0]))int((1)/(sqrt(a(a[0])^(2)*(cos(theta))^(2)+ g(g[0])^(2)*(sin(theta))^(2))), theta = 0..Pi/ 2) |
Error |
Failure | Error | Skip | - |
| 19.8.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\int_{0}^{\pi/2}\frac{\diff{\theta}}{\sqrt{a_{0}^{2}\cos^{2}@@{\theta}+g_{0}^{2}\sin^{2}@@{\theta}}} = \frac{1}{\pi}\int_{0}^{\infty}\frac{\diff{t}}{\sqrt{t(t+a_{0}^{2})(t+g_{0}^{2})}}} | int((1)/(sqrt(a(a[0])^(2)*(cos(theta))^(2)+ g(g[0])^(2)*(sin(theta))^(2))), theta = 0..Pi/ 2)int((1)/(sqrt(t*(t + a(a[0])^(2))*(t + g(g[0])^(2)))), t = 0..infinity) |
Integrate[Divide[1,Sqrt[a(Subscript[a, 0])^(2)*(Cos[\[Theta]])^(2)+ g(Subscript[g, 0])^(2)*(Sin[\[Theta]])^(2)]], {\[Theta], 0, Pi/ 2}]Integrate[Divide[1,Sqrt[t*(t + a(Subscript[a, 0])^(2))*(t + g(Subscript[g, 0])^(2))]], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 19.8.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = \frac{\pi}{2\!\AGM@{1}{k^{\prime}}}} | EllipticK(k)=(Pi)/(2*GaussAGM(1, sqrt(1 - (k)^(2)))) |
Error |
Failure | Error | Skip | - |
| 19.8.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{k} = \frac{\pi}{2\!\AGM@{1}{k^{\prime}}}\left(a_{0}^{2}-\sum_{n=0}^{\infty}2^{n-1}c_{n}^{2}\right)} | EllipticE(k)(a(a[0])^(2)- sum((2)^(n - 1)* c(c[n])^(2), n = 0..infinity)) |
Error |
Failure | Error | Skip | - |
| 19.8.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\pi}{2\!\AGM@{1}{k^{\prime}}}\left(a_{0}^{2}-\sum_{n=0}^{\infty}2^{n-1}c_{n}^{2}\right) = \compellintKk@{k}\left(a_{1}^{2}-\sum_{n=2}^{\infty}2^{n-1}c_{n}^{2}\right)} | (a(a[0])^(2)- sum((2)^(n - 1)* c(c[n])^(2), n = 0..infinity))(a(a[1])^(2)- sum((2)^(n - 1)* c(c[n])^(2), n = 2..infinity)) |
Error |
Failure | Error | Skip | - |
| 19.8.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintPik@{\alpha^{2}}{k} = \frac{\pi}{4\!\AGM@{1}{k^{\prime}}}\left(2+\frac{\alpha^{2}}{1-\alpha^{2}}\sum_{n=0}^{\infty}Q_{n}\right)} | EllipticPi((alpha)^(2), k)=(Pi)/(4*GaussAGM(1, sqrt(1 - (k)^(2))))*(2 +((alpha)^(2))/(1 - (alpha)^(2))*sum(Q[n], n = 0..infinity)) |
Error |
Failure | Error | Skip | - |
| 19.8.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintPik@{\alpha^{2}}{k} = \frac{\pi}{4\!\AGM@{1}{k^{\prime}}}\frac{k^{2}}{k^{2}-\alpha^{2}}\sum_{n=0}^{\infty}Q_{n}} | EllipticPi((alpha)^(2), k)=(Pi)/(4*GaussAGM(1, sqrt(1 - (k)^(2))))*((k)^(2))/((k)^(2)- (alpha)^(2))*sum(Q[n], n = 0..infinity) |
Error |
Failure | Error | Skip | - |
| 19.8#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi_{1} = \phi+\atan@{k^{\prime}\tan@@{\phi}}} | phi[1]= phi + arctan(sqrt(1 - (k)^(2))*tan(phi)) |
Subscript[\[Phi], 1]= \[Phi]+ ArcTan[Sqrt[1 - (k)^(2)]*Tan[\[Phi]]] |
Failure | Failure | Fail 1.094670290-.1488495390e-1*I <- {phi = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)+I*2^(1/2), k = 2}1.264955024-.1049221987e-1*I <- {phi = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)+I*2^(1/2), k = 3}-2.828427124*I <- {phi = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)-I*2^(1/2), k = 1}1.094670290-2.843312078*I <- {phi = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)-I*2^(1/2), k = 2}... skip entries to safe data |
Successful |
| 19.8#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi+\atan@{k^{\prime}\tan@@{\phi}} = \asin@{(1+k^{\prime})\frac{\sin@@{\phi}\cos@@{\phi}}{\sqrt{1-k^{2}\sin^{2}@@{\phi}}}}} | phi + arctan(sqrt(1 - (k)^(2))*tan(phi))= arcsin((1 +sqrt(1 - (k)^(2)))*(sin(phi)*cos(phi))/(sqrt(1 - (k)^(2)* (sin(phi))^(2)))) |
\[Phi]+ ArcTan[Sqrt[1 - (k)^(2)]*Tan[\[Phi]]]= ArcSin[(1 +Sqrt[1 - (k)^(2)])*Divide[Sin[\[Phi]]*Cos[\[Phi]],Sqrt[1 - (k)^(2)* (Sin[\[Phi]])^(2)]]] |
Failure | Failure | Fail 1.876175051-2.798657216*I <- {phi = 2^(1/2)-I*2^(1/2), k = 2}2.216744518-2.807442684*I <- {phi = 2^(1/2)-I*2^(1/2), k = 3}-1.876175051+2.798657216*I <- {phi = -2^(1/2)+I*2^(1/2), k = 2}-2.216744518+2.807442684*I <- {phi = -2^(1/2)+I*2^(1/2), k = 3} |
Fail
Complex[1.8761750519919396, -2.798657217034252] <- {Rule[k, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[2.216744518353377, -2.8074426850863325] <- {Rule[k, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.8761750519919396, 2.798657217034252] <- {Rule[k, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.216744518353377, 2.8074426850863325] <- {Rule[k, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 19.8#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = (1+k_{1})\compellintKk@{k_{1}}} | EllipticK(k)=(1 + k[1])* EllipticK(k[1]) |
EllipticK[(k)^2]=(1 + Subscript[k, 1])* EllipticK[(Subscript[k, 1])^2] |
Failure | Failure | Error | Fail
Complex[-1.685750354812596, -1.0782578237498217] <- {Rule[k, 2]}Complex[-1.6173867356247322, -0.842875177406298] <- {Rule[k, 3]} |
| 19.8#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{k} = (1+k^{\prime})\compellintEk@{k_{1}}-k^{\prime}\compellintKk@{k}} | EllipticE(k)=(1 +sqrt(1 - (k)^(2)))* EllipticE(k[1])-sqrt(1 - (k)^(2))*EllipticK(k) |
EllipticE[(k)^2]=(1 +Sqrt[1 - (k)^(2)])* EllipticE[(Subscript[k, 1])^2]-Sqrt[1 - (k)^(2)]*EllipticK[(k)^2] |
Failure | Failure | Error | Fail
Complex[0.8064340115138717, 0.2620377583302733] <- {Rule[k, 2]}Complex[1.1233981879763189, -0.2935366302694502] <- {Rule[k, 3]} |
| 19.8#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{k} = \tfrac{1}{2}(1+k_{1})\incellintFk@{\phi_{1}}{k_{1}}} | EllipticF(sin(phi), k)=(1)/(2)*(1 + k[1])* EllipticF(sin(phi[1]), k[1]) |
EllipticF[\[Phi], (k)^2]=Divide[1,2]*(1 + Subscript[k, 1])* EllipticF[Subscript[\[Phi], 1], (Subscript[k, 1])^2] |
Failure | Failure | Fail .2918190600+.64188702e-1*I <- {phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)+I*2^(1/2), k = 1}.407379233e-1-.384751455*I <- {phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)+I*2^(1/2), k = 2}-.393423424e-1-.6075011659*I <- {phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)+I*2^(1/2), k = 3}-1.145001001+.5724275385*I <- {phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Successful |
| 19.8#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} = \tfrac{1}{2}(1+k^{\prime})\incellintEk@{\phi_{1}}{k_{1}}-k^{\prime}\incellintFk@{\phi}{k}+\tfrac{1}{2}(1-k^{\prime})\sin@@{\phi_{1}}} | EllipticE(sin(phi), k)=(1)/(2)*(1 +sqrt(1 - (k)^(2)))* EllipticE(sin(phi[1]), k[1])-sqrt(1 - (k)^(2))*EllipticF(sin(phi), k)+(1)/(2)*(1 -sqrt(1 - (k)^(2)))* sin(phi[1]) |
EllipticE[\[Phi], (k)^2]=Divide[1,2]*(1 +Sqrt[1 - (k)^(2)])* EllipticE[Subscript[\[Phi], 1], (Subscript[k, 1])^2]-Sqrt[1 - (k)^(2)]*EllipticF[\[Phi], (k)^2]+Divide[1,2]*(1 -Sqrt[1 - (k)^(2)])* Sin[Subscript[\[Phi], 1]] |
Failure | Failure | Fail -.942116029-.9810550268*I <- {phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)+I*2^(1/2), k = 1}.743033975-3.185064608*I <- {phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)+I*2^(1/2), k = 2}3.178569085-4.992225484*I <- {phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)+I*2^(1/2), k = 3}1.575776580+2.225504017*I <- {phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Successful |
| 19.8#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{1} = \csc^{2}@@{\phi_{1}}} | c[1]= (csc(phi[1]))^(2) |
Subscript[c, 1]= (Csc[Subscript[\[Phi], 1]])^(2) |
Failure | Failure | Fail 1.210530730+1.472494686*I <- {c[1] = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)+I*2^(1/2)}1.210530730+1.355932438*I <- {c[1] = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)-I*2^(1/2)}1.210530730+1.472494686*I <- {c[1] = 2^(1/2)+I*2^(1/2), phi[1] = -2^(1/2)-I*2^(1/2)}1.210530730+1.355932438*I <- {c[1] = 2^(1/2)+I*2^(1/2), phi[1] = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.210530730056432, 1.472494685832072] <- {Rule[Subscript[c, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ϕ, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.210530730056432, 1.3559324389141183] <- {Rule[Subscript[c, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ϕ, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.210530730056432, 1.472494685832072] <- {Rule[Subscript[c, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ϕ, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.210530730056432, 1.3559324389141183] <- {Rule[Subscript[c, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ϕ, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.8#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\phi_{2} = \phi+\asin@{k\sin@@{\phi}}} | 2*phi[2]= phi + arcsin(k*sin(phi)) |
2*Subscript[\[Phi], 2]= \[Phi]+ ArcSin[k*Sin[\[Phi]]] |
Failure | Failure | Fail -.13450037e-1-.735044026*I <- {phi = 2^(1/2)+I*2^(1/2), phi[2] = 2^(1/2)+I*2^(1/2), k = 2}-.15590800e-1-1.147765401*I <- {phi = 2^(1/2)+I*2^(1/2), phi[2] = 2^(1/2)+I*2^(1/2), k = 3}-5.656854248*I <- {phi = 2^(1/2)+I*2^(1/2), phi[2] = 2^(1/2)-I*2^(1/2), k = 1}-.13450037e-1-6.391898274*I <- {phi = 2^(1/2)+I*2^(1/2), phi[2] = 2^(1/2)-I*2^(1/2), k = 2}... skip entries to safe data |
Successful |
| 19.8#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{k} = \frac{2}{1+k}\incellintFk@{\phi_{2}}{k_{2}}} | EllipticF(sin(phi), k)=(2)/(1 + k)*EllipticF(sin(phi[2]), k[2]) |
EllipticF[\[Phi], (k)^2]=Divide[2,1 + k]*EllipticF[Subscript[\[Phi], 2], (Subscript[k, 2])^2] |
Failure | Failure | Fail -.1478755578+.6820014149*I <- {phi = 2^(1/2)+I*2^(1/2), k[2] = 2^(1/2)+I*2^(1/2), phi[2] = 2^(1/2)+I*2^(1/2), k = 1}-.1866400363+.5025213980*I <- {phi = 2^(1/2)+I*2^(1/2), k[2] = 2^(1/2)+I*2^(1/2), phi[2] = 2^(1/2)+I*2^(1/2), k = 2}-.1605619730+.4145017571*I <- {phi = 2^(1/2)+I*2^(1/2), k[2] = 2^(1/2)+I*2^(1/2), phi[2] = 2^(1/2)+I*2^(1/2), k = 3}-.8504514854+1.514599702*I <- {phi = 2^(1/2)+I*2^(1/2), k[2] = 2^(1/2)+I*2^(1/2), phi[2] = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Successful |
| 19.8#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} = (1+k)\incellintEk@{\phi_{2}}{k_{2}}+(1-k)\incellintFk@{\phi_{2}}{k_{2}}-k\sin@@{\phi}} | EllipticE(sin(phi), k)=(1 + k)* EllipticE(sin(phi[2]), k[2])+(1 - k)* EllipticF(sin(phi[2]), k[2])- k*sin(phi) |
EllipticE[\[Phi], (k)^2]=(1 + k)* EllipticE[Subscript[\[Phi], 2], (Subscript[k, 2])^2]+(1 - k)* EllipticF[Subscript[\[Phi], 2], (Subscript[k, 2])^2]- k*Sin[\[Phi]] |
Failure | Failure | Fail -3.768464116-3.924220109*I <- {phi = 2^(1/2)+I*2^(1/2), k[2] = 2^(1/2)+I*2^(1/2), phi[2] = 2^(1/2)+I*2^(1/2), k = 1}-3.226003445-6.062382948*I <- {phi = 2^(1/2)+I*2^(1/2), k[2] = 2^(1/2)+I*2^(1/2), phi[2] = 2^(1/2)+I*2^(1/2), k = 2}-2.601575251-8.024788758*I <- {phi = 2^(1/2)+I*2^(1/2), k[2] = 2^(1/2)+I*2^(1/2), phi[2] = 2^(1/2)+I*2^(1/2), k = 3}6.303106322+7.694970191*I <- {phi = 2^(1/2)+I*2^(1/2), k[2] = 2^(1/2)+I*2^(1/2), phi[2] = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Successful |
| 19.8#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{\psi_{1}} = \frac{(1+k^{\prime})\sin@@{\phi}}{1+\Delta}} | sin(psi[1])=((1 +sqrt(1 - (k)^(2)))* sin(phi))/(1 + Delta) |
Sin[Subscript[\[Psi], 1]]=Divide[(1 +Sqrt[1 - (k)^(2)])* Sin[\[Phi]],1 + \[CapitalDelta]] |
Failure | Failure | Fail 1.433508616+.5973782105*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi[1] = 2^(1/2)+I*2^(1/2), k = 1}.921485403-.6462809029*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi[1] = 2^(1/2)+I*2^(1/2), k = 2}.597378210-1.433508616*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi[1] = 2^(1/2)+I*2^(1/2), k = 3}1.433508616-.61447305e-2*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi[1] = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[1.4335086174698362, 0.5973782103005845] <- {Rule[k, 1], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ψ, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.921485403472285, -0.6462809030436932] <- {Rule[k, 2], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ψ, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.5973782103005842, -1.433508617469836] <- {Rule[k, 3], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ψ, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4335086174698362, -0.006144729434937324] <- {Rule[k, 1], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ψ, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.8#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Delta = \sqrt{1-k^{2}\sin^{2}@@{\phi}}} | Delta =sqrt(1 - (k)^(2)* (sin(phi))^(2)) |
\[CapitalDelta]=Sqrt[1 - (k)^(2)* (Sin[\[Phi]])^(2)] |
Failure | Failure | Fail 1.074539570+3.325606671*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k = 1}.7940624558+5.601906026*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k = 2}.4980873551+7.792433846*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k = 3}1.074539570-.497179547*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[1.0745395706783705, 3.3256066725373055] <- {Rule[k, 1], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.7940624576072436, 5.601906029178632] <- {Rule[k, 2], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.4980873572993363, 7.792433849582317] <- {Rule[k, 3], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0745395706783705, -0.49717954779111495] <- {Rule[k, 1], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.8#Ex22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{k} = (1+k_{1})\incellintFk@{\psi_{1}}{k_{1}}} | EllipticF(sin(phi), k)=(1 + k[1])* EllipticF(sin(psi[1]), k[1]) |
EllipticF[\[Phi], (k)^2]=(1 + Subscript[k, 1])* EllipticF[Subscript[\[Psi], 1], (Subscript[k, 1])^2] |
Failure | Failure | Fail .945637034e-1-1.362004431*I <- {phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), psi[1] = 2^(1/2)+I*2^(1/2), k = 1}-.1565174333-1.810944588*I <- {phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), psi[1] = 2^(1/2)+I*2^(1/2), k = 2}-.2365976990-2.033694299*I <- {phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), psi[1] = 2^(1/2)+I*2^(1/2), k = 3}-2.779076419-.345526758*I <- {phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), psi[1] = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-0.48907441628770865, -1.4903818357543746] <- {Rule[k, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ψ, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4370593625301775, -1.7478657864319769] <- {Rule[k, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ψ, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.7006101295186067, -1.3166147323299215] <- {Rule[k, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ψ, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.4890744162877091, 4.471145507263124] <- {Rule[k, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ψ, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.8#Ex23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} = (1+k^{\prime})\incellintEk@{\psi_{1}}{k_{1}}-k^{\prime}\incellintFk@{\phi}{k}+(1-\Delta)\cot@@{\phi}} | EllipticE(sin(phi), k)=(1 +sqrt(1 - (k)^(2)))* EllipticE(sin(psi[1]), k[1])-sqrt(1 - (k)^(2))*EllipticF(sin(phi), k)+(1 - Delta)* cot(phi) |
EllipticE[\[Phi], (k)^2]=(1 +Sqrt[1 - (k)^(2)])* EllipticE[Subscript[\[Psi], 1], (Subscript[k, 1])^2]-Sqrt[1 - (k)^(2)]*EllipticF[\[Phi], (k)^2]+(1 - \[CapitalDelta])* Cot[\[Phi]] |
Failure | Failure | Fail -.607875038-2.285836406*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), psi[1] = 2^(1/2)+I*2^(1/2), k = 1}3.299178317-9.848207688*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), psi[1] = 2^(1/2)+I*2^(1/2), k = 2}7.141163056-15.04717488*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), psi[1] = 2^(1/2)+I*2^(1/2), k = 3}4.427910181+3.523758744*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), psi[1] = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Skip |
| 19.8#Ex26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c = \csc^{2}@@{\phi}} | c = (csc(phi))^(2) |
c = (Csc[\[Phi]])^(2) |
Failure | Failure | Fail 1.210530730+1.472494686*I <- {c = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2)}1.210530730+1.355932438*I <- {c = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)-I*2^(1/2)}1.210530730+1.472494686*I <- {c = 2^(1/2)+I*2^(1/2), phi = -2^(1/2)-I*2^(1/2)}1.210530730+1.355932438*I <- {c = 2^(1/2)+I*2^(1/2), phi = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.210530730056432, 1.472494685832072] <- {Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.210530730056432, 1.3559324389141183] <- {Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.210530730056432, 1.472494685832072] <- {Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.210530730056432, 1.3559324389141183] <- {Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.9#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 <= \compellintEk@{k}} | 1 < = EllipticE(k) |
1 < = EllipticE[(k)^2] |
Failure | Failure | Successful | Successful |
| 19.9#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{k} <= \pi/2} | EllipticE(k)< = Pi/ 2 |
EllipticE[(k)^2]< = Pi/ 2 |
Failure | Failure | Successful | Successful |
| 19.9#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 <= (2/\pi)\sqrt{1-\alpha^{2}}\compellintPik@{\alpha^{2}}{k}\leq 1/k^{\prime}} | 1 < =(2/ Pi)*sqrt(1 - (alpha)^(2))*EllipticPi((alpha)^(2), k)<= 1/sqrt(1 - (k)^(2)) |
1 < =(2/ Pi)*Sqrt[1 - (\[Alpha])^(2)]*EllipticPi[(\[Alpha])^(2), (k)^2]<= 1/Sqrt[1 - (k)^(2)] |
Failure | Failure | Error | Successful |
| 19.9.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1+\frac{{k^{\prime}}^{2}}{8} < \frac{\compellintKk@{k}}{\ln@{4/k^{\prime}}}} | 1 +(1 - (k)^(2))/(8)<(EllipticK(k))/(ln(4/sqrt(1 - (k)^(2)))) |
1 +Divide[1 - (k)^(2),8]<Divide[EllipticK[(k)^2],Log[4/Sqrt[1 - (k)^(2)]]] |
Failure | Failure | Error | Successful |
| 19.9.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\compellintKk@{k}}{\ln@{4/k^{\prime}}} < 1+\frac{{k^{\prime}}^{2}}{4}} | (EllipticK(k))/(ln(4/sqrt(1 - (k)^(2))))< 1 +(1 - (k)^(2))/(4) |
Divide[EllipticK[(k)^2],Log[4/Sqrt[1 - (k)^(2)]]]< 1 +Divide[1 - (k)^(2),4] |
Failure | Failure | Error | Successful |
| 19.9.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 9+\frac{k^{2}{k^{\prime}}^{2}}{8} < \frac{(8+k^{2})\compellintKk@{k}}{\ln@{4/k^{\prime}}}} | 9 +((k)^(2)* 1 - (k)^(2))/(8)<((8 + (k)^(2))* EllipticK(k))/(ln(4/sqrt(1 - (k)^(2)))) |
9 +Divide[(k)^(2)* 1 - (k)^(2),8]<Divide[(8 + (k)^(2))* EllipticK[(k)^2],Log[4/Sqrt[1 - (k)^(2)]]] |
Failure | Failure | Error | Successful |
| 19.9.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(8+k^{2})\compellintKk@{k}}{\ln@{4/k^{\prime}}} < 9.096} | ((8 + (k)^(2))* EllipticK(k))/(ln(4/sqrt(1 - (k)^(2))))< 9.096 |
Divide[(8 + (k)^(2))* EllipticK[(k)^2],Log[4/Sqrt[1 - (k)^(2)]]]< 9.096 |
Failure | Failure | Error | Successful |
| 19.9.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{1+{k^{\prime}}^{3/2}}{2}\right)^{2/3} <= \frac{2}{\pi}\compellintEk@{k}} | ((1 +(sqrt(1 - (k)^(2)))^(3/ 2))/(2))^(2/ 3)< =(2)/(Pi)*EllipticE(k) |
(Divide[1 +(Sqrt[1 - (k)^(2)])^(3/ 2),2])^(2/ 3)< =Divide[2,Pi]*EllipticE[(k)^2] |
Failure | Failure | Successful | Successful |
| 19.9.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\compellintEk@{k} <= \left(\frac{1+{k^{\prime}}^{2}}{2}\right)^{1/2}} | (2)/(Pi)*EllipticE(k)< =((1 + 1 - (k)^(2))/(2))^(1/ 2) |
Divide[2,Pi]*EllipticE[(k)^2]< =(Divide[1 + 1 - (k)^(2),2])^(1/ 2) |
Failure | Failure | Successful | Successful |
| 19.9.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{\frac{(1+\sqrt{k^{\prime}})^{2}}{k}} < \frac{\pi\ccompellintKk@{k}}{2\!\compellintKk@{k}}} | ln(((1 +sqrt(sqrt(1 - (k)^(2))))^(2))/(k))<(Pi*EllipticCK(k))/(2*EllipticK(k)) |
Log[Divide[(1 +Sqrt[Sqrt[1 - (k)^(2)]])^(2),k]]<Divide[Pi*EllipticK[1-(k)^2],2*EllipticK[(k)^2]] |
Failure | Failure | Error | Successful |
| 19.9.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\pi\ccompellintKk@{k}}{2\!\compellintKk@{k}} < \ln@@{\frac{2(1+k^{\prime})}{k}}} | (Pi*EllipticCK(k))/(2*EllipticK(k))< ln((2*(1 +sqrt(1 - (k)^(2))))/(k)) |
Divide[Pi*EllipticK[1-(k)^2],2*EllipticK[(k)^2]]< Log[Divide[2*(1 +Sqrt[1 - (k)^(2)]),k]] |
Failure | Failure | Error | Successful |
| 19.9.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-\tfrac{3}{4}k^{2})^{-1/2} < \frac{4}{\pi k^{2}}(\compellintKk@{k}-\compellintEk@{k})} | (1 -(3)/(4)*(k)^(2))^(- 1/ 2)<(4)/(Pi*(k)^(2))*(EllipticK(k)- EllipticE(k)) |
(1 -Divide[3,4]*(k)^(2))^(- 1/ 2)<Divide[4,Pi*(k)^(2)]*(EllipticK[(k)^2]- EllipticE[(k)^2]) |
Failure | Failure | Error | Successful |
| 19.9.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{4}{\pi k^{2}}(\compellintKk@{k}-\compellintEk@{k}) < (k^{\prime})^{-3/4}} | (4)/(Pi*(k)^(2))*(EllipticK(k)- EllipticE(k))<(sqrt(1 - (k)^(2)))^(- 3/ 4) |
Divide[4,Pi*(k)^(2)]*(EllipticK[(k)^2]- EllipticE[(k)^2])<(Sqrt[1 - (k)^(2)])^(- 3/ 4) |
Failure | Failure | Error | Successful |
| 19.9.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-\tfrac{1}{4}k^{2})^{-1/2} < \frac{4}{\pi k^{2}}(\compellintEk@{k}-{k^{\prime}}^{2}\compellintKk@{k})} | (1 -(1)/(4)*(k)^(2))^(- 1/ 2)<(4)/(Pi*(k)^(2))*(EllipticE(k)- 1 - (k)^(2)* EllipticK(k)) |
(1 -Divide[1,4]*(k)^(2))^(- 1/ 2)<Divide[4,Pi*(k)^(2)]*(EllipticE[(k)^2]- 1 - (k)^(2)* EllipticK[(k)^2]) |
Failure | Failure | Error | Successful |
| 19.9.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{\prime} < \frac{\compellintEk@{k}}{\compellintKk@{k}}} | sqrt(1 - (k)^(2))<(EllipticE(k))/(EllipticK(k)) |
Sqrt[1 - (k)^(2)]<Divide[EllipticE[(k)^2],EllipticK[(k)^2]] |
Failure | Failure | Error | Successful |
| 19.9.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\compellintEk@{k}}{\compellintKk@{k}} < \left(\frac{1+k^{\prime}}{2}\right)^{2}} | (EllipticE(k))/(EllipticK(k))<((1 +sqrt(1 - (k)^(2)))/(2))^(2) |
Divide[EllipticE[(k)^2],EllipticK[(k)^2]]<(Divide[1 +Sqrt[1 - (k)^(2)],2])^(2) |
Failure | Failure | Error | Successful |
| 19.9.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L(a,b) = 4a\compellintEk@{k}} | L*(a , b)= 4*a*EllipticE(k) |
L*(a , b)= 4*a*EllipticE[(k)^2] |
Failure | Failure | Skip | Error |
| 19.9.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi <= \incellintFk@{\phi}{k}} | phi < = EllipticF(sin(phi), k) |
\[Phi]< = EllipticF[\[Phi], (k)^2] |
Failure | Failure | Successful | Successful |
| 19.9.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} <= \phi} | EllipticE(sin(phi), k)< = phi |
EllipticE[\[Phi], (k)^2]< = \[Phi] |
Failure | Failure | Successful | Successful |
| 19.9.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{\alpha^{2}}{0} <= \incellintPik@{\phi}{\alpha^{2}}{k}} | EllipticPi(sin(phi), (alpha)^(2), 0)< = EllipticPi(sin(phi), (alpha)^(2), k) |
EllipticPi[(\[Alpha])^(2), \[Phi],(0)^2]< = EllipticPi[(\[Alpha])^(2), \[Phi],(k)^2] |
Failure | Failure | Successful | Successful |
| 19.9.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{3}{1+\Delta+\cos@@{\phi}} < \frac{\incellintFk@{\phi}{k}}{\sin@@{\phi}}} | (3)/(1 + Delta + cos(phi))<(EllipticF(sin(phi), k))/(sin(phi)) |
Divide[3,1 + \[CapitalDelta]+ Cos[\[Phi]]]<Divide[EllipticF[\[Phi], (k)^2],Sin[\[Phi]]] |
Failure | Failure | Successful | Successful |
| 19.9.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\incellintFk@{\phi}{k}}{\sin@@{\phi}} < \frac{1}{(\Delta\cos@@{\phi})^{1/3}}} | (EllipticF(sin(phi), k))/(sin(phi))<(1)/((Delta*cos(phi))^(1/ 3)) |
Divide[EllipticF[\[Phi], (k)^2],Sin[\[Phi]]]<Divide[1,(\[CapitalDelta]*Cos[\[Phi]])^(1/ 3)] |
Failure | Failure | Successful | Successful |
| 19.9.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 < \incellintFk@{\phi}{k}\bigg{/}\left((\sin@@{\phi})\ln@{\frac{4}{\Delta+\cos@@{\phi}}}\right)} | 1 < EllipticF(sin(phi), k)/((sin(phi))*ln((4)/(Delta + cos(phi)))) |
1 < EllipticF[\[Phi], (k)^2]/((Sin[\[Phi]])*Log[Divide[4,\[CapitalDelta]+ Cos[\[Phi]]]]) |
Failure | Failure | Successful | Successful |
| 19.9.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{k}\bigg{/}\left((\sin@@{\phi})\ln@{\frac{4}{\Delta+\cos@@{\phi}}}\right) < \frac{4}{2+(1+k^{2})\sin^{2}@@{\phi}}} | EllipticF(sin(phi), k)/((sin(phi))*ln((4)/(Delta + cos(phi))))<(4)/(2 +(1 + (k)^(2))* (sin(phi))^(2)) |
EllipticF[\[Phi], (k)^2]/((Sin[\[Phi]])*Log[Divide[4,\[CapitalDelta]+ Cos[\[Phi]]]])<Divide[4,2 +(1 + (k)^(2))* (Sin[\[Phi]])^(2)] |
Failure | Failure | Successful | Successful |
| 19.9.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L <= \incellintFk@{\phi}{k}} | L < = EllipticF(sin(phi), k) |
L < = EllipticF[\[Phi], (k)^2] |
Failure | Failure | Successful | Successful |
| 19.9.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{k} <= \sqrt{UL}} | EllipticF(sin(phi), k)< =sqrt(U*L) |
EllipticF[\[Phi], (k)^2]< =Sqrt[U*L] |
Failure | Failure | Successful | Successful |
| 19.9.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{UL} <= \tfrac{1}{2}(U+L)} | sqrt(U*L)< =(1)/(2)*(U + L) |
Sqrt[U*L]< =Divide[1,2]*(U + L) |
Failure | Failure | Skip | Successful |
| 19.9.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}(U+L) <= U} | (1)/(2)*(U + L)< = U |
Divide[1,2]*(U + L)< = U |
Failure | Failure | Skip | Successful |
| 19.9#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L = (1/\sigma)\atanh@{\sigma\sin@@{\phi}}} | L =(1/ sigma)* arctanh(sigma*sin(phi)) |
L =(1/ \[Sigma])* ArcTanh[\[Sigma]*Sin[\[Phi]]] |
Failure | Failure | Fail .8766496524+.9719354625*I <- {L = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2)}.8447671788+1.854846236*I <- {L = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2)}.8766496524+.9719354625*I <- {L = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2)}.8447671788+1.854846236*I <- {L = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[0.8766496526774387, 0.9719354626867103] <- {Rule[L, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8447671793191418, 0.9735808886528274] <- {Rule[L, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.9517774720687515, 1.85649166205948] <- {Rule[L, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.9836599454270485, 1.8548462360933629] <- {Rule[L, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.9#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U = \tfrac{1}{2}\atanh@{\sin@@{\phi}}+\tfrac{1}{2}k^{-1}\atanh@{k\sin@@{\phi}}} | U =(1)/(2)*arctanh(sin(phi))+(1)/(2)*(k)^(- 1)* arctanh(k*sin(phi)) |
U =Divide[1,2]*ArcTanh[Sin[\[Phi]]]+Divide[1,2]*(k)^(- 1)* ArcTanh[k*Sin[\[Phi]]] |
Failure | Failure | Fail .9251391454-.76168273e-1*I <- {U = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k = 1}1.111745370+.2847489883*I <- {U = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k = 2}1.144167573+.4108582524*I <- {U = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), k = 3}.9251391454+2.904595397*I <- {U = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[0.9251391460853864, -0.0761682733812794] <- {Rule[k, 1], Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.1117453704027949, 0.2847489881021125] <- {Rule[k, 2], Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.1441675729373713, 0.41085825249377617] <- {Rule[k, 3], Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.9251391460853866, 2.9045953981274697] <- {Rule[k, 1], Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.11.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\theta}{k}+\incellintFk@{\phi}{k} = \incellintFk@{\psi}{k}} | EllipticF(sin(theta), k)+ EllipticF(sin(phi), k)= EllipticF(sin(psi), k) |
EllipticF[\[Theta], (k)^2]+ EllipticF[\[Phi], (k)^2]= EllipticF[\[Psi], (k)^2] |
Failure | Failure | Fail .4890744166+1.490381835*I <- {phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 1}.2379932799+1.041441678*I <- {phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 2}.1579130142+.8186919671*I <- {phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 3}.4890744166-1.490381835*I <- {phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[0.48907441628770865, 1.4903818357543746] <- {Rule[k, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.23799327973838402, 1.0414416780368256] <- {Rule[k, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.15791301410980507, 0.8186919671649275] <- {Rule[k, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.4890744162877084, 4.471145507263124] <- {Rule[k, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.11.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\theta}{k}+\incellintEk@{\phi}{k} = \incellintEk@{\psi}{k}+k^{2}\sin@@{\theta}\sin@@{\phi}\sin@@{\psi}} | EllipticE(sin(theta), k)+ EllipticE(sin(phi), k)= EllipticE(sin(psi), k)+ (k)^(2)* sin(theta)*sin(phi)*sin(psi) |
EllipticE[\[Theta], (k)^2]+ EllipticE[\[Phi], (k)^2]= EllipticE[\[Psi], (k)^2]+ (k)^(2)* Sin[\[Theta]]*Sin[\[Phi]]*Sin[\[Psi]] |
Failure | Failure | Fail -7.220392390-3.861416894*I <- {phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 1}-33.54643343-17.33538519*I <- {phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 2}-78.53436280-38.95995319*I <- {phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 3}-8.004067570-1.726125452*I <- {phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Skip |
| 19.11#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{\psi} = \frac{(\sin@@{\theta}\cos@@{\phi})\Delta(\phi)+(\sin@@{\phi}\cos@@{\theta})\Delta(\theta)}{1-k^{2}\sin^{2}@@{\theta}\sin^{2}@@{\phi}}} | sin(psi)=((sin(theta)*cos(phi))* Delta*(phi)+(sin(phi)*cos(theta))* Delta*(theta))/(1 - (k)^(2)* (sin(theta))^(2)* (sin(phi))^(2)) |
Sin[\[Psi]]=Divide[(Sin[\[Theta]]*Cos[\[Phi]])* \[CapitalDelta]*(\[Phi])+(Sin[\[Phi]]*Cos[\[Theta]])* \[CapitalDelta]*(\[Theta]),1 - (k)^(2)* (Sin[\[Theta]])^(2)* (Sin[\[Phi]])^(2)] |
Failure | Failure | Fail 3.669776527-.1132600603*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 1}2.522072859+.2078762259*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 2}2.315484084+.2608036709*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 3}2.972771438+1.122997368*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Skip |
| 19.11#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Delta(\theta) = \sqrt{1-k^{2}\sin^{2}@@{\theta}}} | Delta*(theta)=sqrt(1 - (k)^(2)* (sin(theta))^(2)) |
\[CapitalDelta]*(\[Theta])=Sqrt[1 - (k)^(2)* (Sin[\[Theta]])^(2)] |
Failure | Failure | Fail -.3396739925+5.911393107*I <- {Delta = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 1}-.6201511062+8.187692462*I <- {Delta = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 2}-.9161262069+10.37822028*I <- {Delta = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 3}3.660326006-1.911393109*I <- {Delta = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-0.33967399169472473, 5.9113931101642105] <- {Rule[k, 1], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.6201511047658516, 8.187692466805537] <- {Rule[k, 2], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.9161262050737589, 10.378220287209222] <- {Rule[k, 3], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.660326008305275, -1.91139311016421] <- {Rule[k, 1], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.11#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\psi} = \frac{\cos@@{\theta}\cos@@{\phi}-(\sin@@{\theta}\sin@@{\phi})\Delta(\theta)\Delta(\phi)}{1-k^{2}\sin^{2}@@{\theta}\sin^{2}@@{\phi}}} | cos(psi)=(cos(theta)*cos(phi)-(sin(theta)*sin(phi))* Delta*(theta)* Delta*(phi))/(1 - (k)^(2)* (sin(theta))^(2)* (sin(phi))^(2)) |
Cos[\[Psi]]=Divide[Cos[\[Theta]]*Cos[\[Phi]]-(Sin[\[Theta]]*Sin[\[Phi]])* \[CapitalDelta]*(\[Theta])* \[CapitalDelta]*(\[Phi]),1 - (k)^(2)* (Sin[\[Theta]])^(2)* (Sin[\[Phi]])^(2)] |
Failure | Failure | Fail 3.530512453-2.923665161*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 1}1.119055805-2.142711452*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 2}.6845705541-2.012504035*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 3}.5167796909-5.460396276*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Skip |
| 19.11#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@{\tfrac{1}{2}\psi} = \frac{(\sin@@{\theta})\Delta(\phi)+(\sin@@{\phi})\Delta(\theta)}{\cos@@{\theta}+\cos@@{\phi}}} | tan((1)/(2)*psi)=((sin(theta))* Delta*(phi)+(sin(phi))* Delta*(theta))/(cos(theta)+ cos(phi)) |
Tan[Divide[1,2]*\[Psi]]=Divide[(Sin[\[Theta]])* \[CapitalDelta]*(\[Phi])+(Sin[\[Phi]])* \[CapitalDelta]*(\[Theta]),Cos[\[Theta]]+ Cos[\[Phi]]] |
Failure | Failure | Fail 4.896680821+.6655470386*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2)}-14.02182515-13.61597715*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2)}-4.050312273+.9925175081*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2)}14.86819369+15.27404169*I <- {Delta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[4.896680823473283, 0.6655470393878908] <- {Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.896680823473283, -0.992517507894449] <- {Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.050312275733391, -0.992517507894449] <- {Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.050312275733391, 0.6655470393878908] <- {Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.11#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma = ((\csc^{2}@@{\theta})-\alpha^{2})((\csc^{2}@@{\phi})-\alpha^{2})((\csc^{2}@@{\psi})-\alpha^{2})} | gamma =(((csc(theta))^(2))- (alpha)^(2))*(((csc(phi))^(2))- (alpha)^(2))*(((csc(psi))^(2))- (alpha)^(2)) |
\[Gamma]=(((Csc[\[Theta]])^(2))- (\[Alpha])^(2))*(((Csc[\[Phi]])^(2))- (\[Alpha])^(2))*(((Csc[\[Psi]])^(2))- (\[Alpha])^(2)) |
Failure | Failure | Fail 10.63251777-66.33335806*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2)}10.43981655-64.41845493*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2)}10.63251777-66.33335806*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2)}10.43981655-64.41845493*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Skip |
| 19.11.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{k} = \compellintKk@{k}-\incellintFk@{\theta}{k}} | EllipticF(sin(phi), k)= EllipticK(k)- EllipticF(sin(theta), k) |
EllipticF[\[Phi], (k)^2]= EllipticK[(k)^2]- EllipticF[\[Theta], (k)^2] |
Failure | Failure | Error | Fail
DirectedInfinity[] <- {Rule[k, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.3668886179295301, 3.161141179823473] <- {Rule[k, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.2233028836553006, 2.480259111736153] <- {Rule[k, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}DirectedInfinity[] <- {Rule[k, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.11.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} = \compellintEk@{k}-\incellintEk@{\theta}{k}+k^{2}\sin@@{\theta}\sin@@{\phi}} | EllipticE(sin(phi), k)= EllipticE(k)- EllipticE(sin(theta), k)+ (k)^(2)* sin(theta)*sin(phi) |
EllipticE[\[Phi], (k)^2]= EllipticE[(k)^2]- EllipticE[\[Theta], (k)^2]+ (k)^(2)* Sin[\[Theta]]*Sin[\[Phi]] |
Failure | Failure | Fail -1.234974115-.6949781160*I <- {phi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 1}-10.67592308-7.903201927*I <- {phi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 2}-29.48202603-17.16755346*I <- {phi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 3}-1.417094085+0.*I <- {phi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-1.234974118270812, -0.6949781151190215] <- {Rule[k, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-10.675923102954668, -7.903201921490194] <- {Rule[k, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-29.48202606417501, -17.167553444002383] <- {Rule[k, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4170940876643146, 0.0] <- {Rule[k, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.11.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@@{\theta} = 1/(k^{\prime}\tan@@{\phi})} | tan(theta)= 1/(sqrt(1 - (k)^(2))*tan(phi)) |
Tan[\[Theta]]= 1/(Sqrt[1 - (k)^(2)]*Tan[\[Phi]]) |
Failure | Failure | Fail Float(infinity)+Float(infinity)*I <- {phi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 1}.5564234783+1.137215141*I <- {phi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 2}.3565812465+1.129911849*I <- {phi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 3}Float(infinity)+Float(infinity)*I <- {phi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
DirectedInfinity[] <- {Rule[k, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.5564234779243372, 1.1372151415780356] <- {Rule[k, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.3565812462431767, 1.1299118490197817] <- {Rule[k, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}DirectedInfinity[] <- {Rule[k, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.11#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma = (1-\alpha^{2})((\csc^{2}@@{\theta})-\alpha^{2})((\csc^{2}@@{\phi})-\alpha^{2})} | gamma =(1 - (alpha)^(2))*(((csc(theta))^(2))- (alpha)^(2))*(((csc(phi))^(2))- (alpha)^(2)) |
\[Gamma]=(1 - (\[Alpha])^(2))*(((Csc[\[Theta]])^(2))- (\[Alpha])^(2))*(((Csc[\[Phi]])^(2))- (\[Alpha])^(2)) |
Failure | Failure | Fail 23.61819217-64.05943146*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2)}23.05018289-62.19100371*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2)}23.61819217-64.05943146*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2)}23.05018289-62.19100371*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[24.455190091722997, -62.64521797387181] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[γ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[23.887180810974133, -60.776790236964885] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[γ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[24.455190091722997, -62.64521797387181] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[γ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[23.887180810974133, -60.776790236964885] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[γ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.11.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\psi}{k} = 2\!\incellintFk@{\theta}{k}} | EllipticF(sin(psi), k)= 2*EllipticF(sin(theta), k) |
EllipticF[\[Psi], (k)^2]= 2*EllipticF[\[Theta], (k)^2] |
Failure | Failure | Fail -.4890744166-1.490381835*I <- {psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 1}-.2379932799-1.041441678*I <- {psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 2}-.1579130142-.8186919671*I <- {psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 3}-.4890744166+4.471145505*I <- {psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-0.48907441628770865, -1.4903818357543746] <- {Rule[k, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.23799327973838402, -1.0414416780368256] <- {Rule[k, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.15791301410980507, -0.8186919671649275] <- {Rule[k, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.4890744162877084, -4.471145507263124] <- {Rule[k, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.11.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\psi}{k} = 2\!\incellintEk@{\theta}{k}-k^{2}\sin^{2}@@{\theta}\sin@@{\psi}} | EllipticE(sin(psi), k)= 2*EllipticE(sin(theta), k)- (k)^(2)* (sin(theta))^(2)* sin(psi) |
EllipticE[\[Psi], (k)^2]= 2*EllipticE[\[Theta], (k)^2]- (k)^(2)* (Sin[\[Theta]])^(2)* Sin[\[Psi]] |
Failure | Failure | Fail 7.220392390+3.861416894*I <- {psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 1}33.54643343+17.33538519*I <- {psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 2}78.53436280+38.95995319*I <- {psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 3}8.004067570-.5190795705*I <- {psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[7.220392409769752, 3.8614168902831674] <- {Rule[k, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[33.54643351078474, 17.335385175946172] <- {Rule[k, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[78.53436298397799, 38.95995315264784] <- {Rule[k, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[8.004067583645242, 0.5190795702179967] <- {Rule[k, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.11.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{\psi} = (\sin@@{2\theta})\Delta(\theta)/(1-k^{2}\sin^{4}@@{\theta})} | sin(psi)=(sin(2*theta))* Delta*(theta)/(1 - (k)^(2)* (sin(theta))^(4)) |
Sin[\[Psi]]=(Sin[2*\[Theta]])* \[CapitalDelta]*(\[Theta])/(1 - (k)^(2)* (Sin[\[Theta]])^(4)) |
Failure | Failure | Fail 3.669776527-.1132600606*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 1}2.522072859+.2078762258*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 2}2.315484084+.2608036708*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 3}1.736514009+1.820002458*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[3.669776527136964, -0.11326005969545538] <- {Rule[k, 1], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.5220728602932043, 0.20787622554236157] <- {Rule[k, 2], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.315484085450414, 0.2608036703182187] <- {Rule[k, 3], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.669776527136964, -0.7167829994309771] <- {Rule[k, 1], Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.11#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\psi} = (\cos@{2\theta}+k^{2}\sin^{4}@@{\theta})/(1-k^{2}\sin^{4}@@{\theta})} | cos(psi)=(cos(2*theta)+ (k)^(2)* (sin(theta))^(4))/(1 - (k)^(2)* (sin(theta))^(4)) |
Cos[\[Psi]]=(Cos[2*\[Theta]]+ (k)^(2)* (Sin[\[Theta]])^(4))/(1 - (k)^(2)* (Sin[\[Theta]])^(4)) |
Failure | Failure | Fail .9973549969-1.831129846*I <- {psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 1}1.256189052-1.893457097*I <- {psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 2}1.302739865-1.903587220*I <- {psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), k = 3}.9973549969-1.991656372*I <- {psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[0.9973549964500539, -1.8311298475339681] <- {Rule[k, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.256189051449076, -1.8934570978250853] <- {Rule[k, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.3027398642662416, -1.9035872217081093] <- {Rule[k, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.9973549964500539, 1.9916563727944525] <- {Rule[k, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.11#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@{\tfrac{1}{2}\psi} = (\tan@@{\theta})\Delta(\theta)} | tan((1)/(2)*psi)=(tan(theta))* Delta*(theta) |
Tan[Divide[1,2]*\[Psi]]=(Tan[\[Theta]])* \[CapitalDelta]*(\[Theta]) |
Failure | Failure | Fail 4.896680820+.6655470387*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2)}.2596990392+5.302528819*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2)}4.896680820+.6655470387*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2)}.2596990392+5.302528819*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Skip |
| 19.11#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{\theta} = (\sin@@{\psi})/\sqrt{(1+\cos@@{\psi})(1+\Delta(\psi))}} | sin(theta)=(sin(psi))/sqrt((1 + cos(psi))*(1 + Delta*(psi))) |
Sin[\[Theta]]=(Sin[\[Psi]])/Sqrt[(1 + Cos[\[Psi]])*(1 + \[CapitalDelta]*(\[Psi]))] |
Failure | Failure | Fail 1.451875812+.3324449118*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2)}1.451875812-.2710780292*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2)}-2.851195268-.2710780292*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2)}-2.851195268+.3324449118*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.4518758131252132, 0.33244491134580767] <- {Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.6336006158758192, 0.6708026401371392] <- {Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[2.3509952614630127, 0.9730892801912212] <- {Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.6279656435120184, 0.97041258344749] <- {Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.11#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\theta} = \sqrt{\frac{(\cos@@{\psi})+\Delta(\psi)}{1+\Delta(\psi)}}} | cos(theta)=sqrt(((cos(psi))+ Delta*(psi))/(1 + Delta*(psi))) |
Cos[\[Theta]]=Sqrt[Divide[(Cos[\[Psi]])+ \[CapitalDelta]*(\[Psi]),1 + \[CapitalDelta]*(\[Psi])]] |
Failure | Failure | Fail -.3760894634-1.941386214*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2)}-.3760894634+1.881400004*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2)}-.3760894634-1.941386214*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2)}-.3760894634+1.881400004*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-0.376089464085568, -1.9413862149418206] <- {Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.6133021347588845, -2.111964043381314] <- {Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.8534281043855928, -1.7991622645406038] <- {Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.7997455475928336, -1.631807314610897] <- {Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.11#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@@{\theta} = \tan@{\tfrac{1}{2}\psi}\sqrt{\frac{1+\cos@@{\psi}}{(\cos@@{\psi})+\Delta(\psi)}}} | tan(theta)= tan((1)/(2)*psi)*sqrt((1 + cos(psi))/((cos(psi))+ Delta*(psi))) |
Tan[\[Theta]]= Tan[Divide[1,2]*\[Psi]]*Sqrt[Divide[1 + Cos[\[Psi]],(Cos[\[Psi]])+ \[CapitalDelta]*(\[Psi])]] |
Failure | Failure | Fail -.9331234340+1.202056207*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2)}-.9331234340-1.034692067*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2)}-1.014866051-1.034692067*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2)}-1.014866051+1.202056207*I <- {Delta = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-0.9331234343650795, 1.202056207743813] <- {Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.40152023420113836, 1.5987346019935262] <- {Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.15411790621097937, 1.6917010756307755] <- {Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.2176994205238692, 0.46809231316455746] <- {Rule[Δ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.11#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma = ((\csc^{2}@@{\theta})-\alpha^{2})^{2}((\csc^{2}@@{\psi})-\alpha^{2})} | gamma =(((csc(theta))^(2))- (alpha)^(2))^(2)*(((csc(psi))^(2))- (alpha)^(2)) |
\[Gamma]=(((Csc[\[Theta]])^(2))- (\[Alpha])^(2))^(2)*(((Csc[\[Psi]])^(2))- (\[Alpha])^(2)) |
Failure | Failure | Fail 10.63251777-66.33335806*I <- {alpha = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2)}10.24988272-62.55869068*I <- {alpha = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2)}10.63251777-66.33335806*I <- {alpha = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2)}10.24988272-62.55869068*I <- {alpha = 2^(1/2)+I*2^(1/2), psi = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[11.46951567083565, -64.91914457079643] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[γ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[11.276814452857538, -63.004241447264036] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[γ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[11.46951567083565, -64.91914457079643] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[γ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[11.276814452857538, -63.004241447264036] <- {Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[γ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ψ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.12.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = \sum_{m=0}^{\infty}\frac{\Pochhammersym{\tfrac{1}{2}}{m}\Pochhammersym{\tfrac{1}{2}}{m}}{m!\;m!}{k^{\prime}}^{2m}\left(\ln@@{\left(\frac{1}{k^{\prime}}\right)}+d(m)\right)} | EllipticK(k)= sum((pochhammer((1)/(2), m)*pochhammer((1)/(2), m))/(factorial(m)*factorial(m))*(sqrt(1 - (k)^(2)))^(2*m)*(ln((1)/(sqrt(1 - (k)^(2))))+ d*(m)), m = 0..infinity) |
EllipticK[(k)^2]= Sum[Divide[Pochhammer[Divide[1,2], m]*Pochhammer[Divide[1,2], m],(m)!*(m)!]*(Sqrt[1 - (k)^(2)])^(2*m)*(Log[Divide[1,Sqrt[1 - (k)^(2)]]]+ d*(m)), {m, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 19.12#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d(m) = \digamma@{1+m}-\digamma@{\tfrac{1}{2}+m}} | d*(m)= Psi(1 + m)- Psi((1)/(2)+ m) |
d*(m)= PolyGamma[1 + m]- PolyGamma[Divide[1,2]+ m] |
Failure | Failure | Fail 1.027919201+1.414213562*I <- {d = 2^(1/2)+I*2^(1/2), m = 1}2.608799430+2.828427124*I <- {d = 2^(1/2)+I*2^(1/2), m = 2}4.089679659+4.242640686*I <- {d = 2^(1/2)+I*2^(1/2), m = 3}1.027919201-1.414213562*I <- {d = 2^(1/2)-I*2^(1/2), m = 1}... skip entries to safe data |
Fail
Complex[1.0279192012532046, 1.4142135623730951] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 1]}Complex[2.6087994302929665, 2.8284271247461903] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 2]}Complex[4.089679659332729, 4.242640687119286] <- {Rule[d, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[m, 3]}Complex[1.0279192012532046, -1.4142135623730951] <- {Rule[d, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[m, 1]}... skip entries to safe data |
| 19.14.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{1}^{x}\frac{\diff{t}}{\sqrt{t^{3}-1}} = 3^{-1/4}\incellintFk@{\phi}{k}} | int((1)/(sqrt((t)^(3)- 1)), t = 1..x)= (3)^(- 1/ 4)* EllipticF(sin(phi), k) |
Integrate[Divide[1,Sqrt[(t)^(3)- 1]], {t, 1, x}]= (3)^(- 1/ 4)* EllipticF[\[Phi], (k)^2] |
Failure | Failure | Skip | Error |
| 19.14.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{1}\frac{\diff{t}}{\sqrt{1-t^{3}}} = 3^{-1/4}\incellintFk@{\phi}{k}} | int((1)/(sqrt(1 - (t)^(3))), t = x..1)= (3)^(- 1/ 4)* EllipticF(sin(phi), k) |
Integrate[Divide[1,Sqrt[1 - (t)^(3)]], {t, x, 1}]= (3)^(- 1/ 4)* EllipticF[\[Phi], (k)^2] |
Failure | Failure | Skip | Successful |
| 19.14.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\frac{\diff{t}}{\sqrt{1+t^{4}}} = \frac{\sign@{x}}{2}\incellintFk@{\phi}{k}} | int((1)/(sqrt(1 + (t)^(4))), t = 0..x)=(signum(x))/(2)*EllipticF(sin(phi), k) |
Integrate[Divide[1,Sqrt[1 + (t)^(4)]], {t, 0, x}]=Divide[Sign[x],2]*EllipticF[\[Phi], (k)^2] |
Failure | Failure | Skip | Successful |
| 19.14.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin^{2}@@{\phi} = \frac{\gamma-\alpha}{U^{2}+\gamma}} | (sin(phi))^(2)=(gamma - alpha)/((U)^(2)+ gamma) |
(Sin[\[Phi]])^(2)=Divide[\[Gamma]- \[Alpha],(U)^(2)+ \[Gamma]] |
Failure | Failure | Fail 4.913966071+1.143498437*I <- {U = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2)}4.913966071-1.453503677*I <- {U = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)-I*2^(1/2)}4.913966071+1.143498437*I <- {U = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), phi = -2^(1/2)-I*2^(1/2)}4.913966071-1.453503677*I <- {U = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), phi = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[4.538045200949385, 1.2985010548545433] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[γ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.538045200949385, -1.2985010548545433] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[γ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.538045200949385, 1.2985010548545433] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[γ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.538045200949385, -1.2985010548545433] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[γ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.14.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin^{2}@@{\phi} = \frac{(\gamma-\alpha)x^{2}}{a_{1}a_{2}+\gamma x^{2}}} | (sin(phi))^(2)=((gamma - alpha)* (x)^(2))/(a[1]*a[2]+ gamma*(x)^(2)) |
(Sin[\[Phi]])^(2)=Divide[(\[Gamma]- \[Alpha])* (x)^(2),Subscript[a, 1]*Subscript[a, 2]+ \[Gamma]*(x)^(2)] |
Failure | Failure | Fail 4.913966071+1.143498437*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), a[1] = 2^(1/2)+I*2^(1/2), a[2] = 2^(1/2)+I*2^(1/2), x = 1}5.961217471+1.282980492*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), a[1] = 2^(1/2)+I*2^(1/2), a[2] = 2^(1/2)+I*2^(1/2), x = 2}6.632730047+2.135696835*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), a[1] = 2^(1/2)+I*2^(1/2), a[2] = 2^(1/2)+I*2^(1/2), x = 3}4.720906995+1.607469143*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), a[1] = 2^(1/2)+I*2^(1/2), a[2] = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Skip |
| 19.14.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin^{2}@@{\phi} = \frac{\gamma-\alpha}{b_{1}b_{2}y^{2}+\gamma}} | (sin(phi))^(2)=(gamma - alpha)/(b[1]*b[2]*(y)^(2)+ gamma) |
(Sin[\[Phi]])^(2)=Divide[\[Gamma]- \[Alpha],Subscript[b, 1]*Subscript[b, 2]*(y)^(2)+ \[Gamma]] |
Failure | Failure | Fail 4.913966071+1.143498437*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), b[1] = 2^(1/2)+I*2^(1/2), b[2] = 2^(1/2)+I*2^(1/2), y = 1}4.628203424+1.249441235*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), b[1] = 2^(1/2)+I*2^(1/2), b[2] = 2^(1/2)+I*2^(1/2), y = 2}4.577691497+1.275886795*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), b[1] = 2^(1/2)+I*2^(1/2), b[2] = 2^(1/2)+I*2^(1/2), y = 3}4.720906995+1.607469143*I <- {alpha = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), b[1] = 2^(1/2)+I*2^(1/2), b[2] = 2^(1/2)-I*2^(1/2), y = 1}... skip entries to safe data |
Skip |
| 19.14.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin^{2}@@{\phi} = \frac{(\gamma-\alpha)(x^{2}-y^{2})}{\gamma(x^{2}-y^{2})-a_{1}(a_{2}+b_{2}x^{2})}} | (sin(phi))^(2)=((gamma - alpha)*((x)^(2)- (y)^(2)))/(gamma*((x)^(2)- (y)^(2))- a[1]*(a[2]+ b[2]*(x)^(2))) |
(Sin[\[Phi]])^(2)=Divide[(\[Gamma]- \[Alpha])*((x)^(2)- (y)^(2)),\[Gamma]*((x)^(2)- (y)^(2))- Subscript[a, 1]*(Subscript[a, 2]+ Subscript[b, 2]*(x)^(2))] |
Failure | Failure | Skip | Skip |
| 19.14.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin^{2}@@{\phi} = \frac{(\gamma-\alpha)(y^{2}-x^{2})}{\gamma(y^{2}-x^{2})-a_{1}(a_{2}+b_{2}y^{2})}} | (sin(phi))^(2)=((gamma - alpha)*((y)^(2)- (x)^(2)))/(gamma*((y)^(2)- (x)^(2))- a[1]*(a[2]+ b[2]*(y)^(2))) |
(Sin[\[Phi]])^(2)=Divide[(\[Gamma]- \[Alpha])*((y)^(2)- (x)^(2)),\[Gamma]*((y)^(2)- (x)^(2))- Subscript[a, 1]*(Subscript[a, 2]+ Subscript[b, 2]*(y)^(2))] |
Failure | Failure | Skip | Skip |
| 19.16.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{z} = \frac{1}{2}\int_{0}^{\infty}\frac{\diff{t}}{s(t)}} | 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+z)), t = 0..infinity)=(1)/(2)*int((1)/(s*(t)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.16#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c = \csc^{2}@@{\phi}} | c = (csc(phi))^(2) |
c = (Csc[\[Phi]])^(2) |
Failure | Failure | Fail 1.210530730+1.472494686*I <- {c = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2)}1.210530730+1.355932438*I <- {c = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)-I*2^(1/2)}1.210530730+1.472494686*I <- {c = 2^(1/2)+I*2^(1/2), phi = -2^(1/2)-I*2^(1/2)}1.210530730+1.355932438*I <- {c = 2^(1/2)+I*2^(1/2), phi = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.210530730056432, 1.472494685832072] <- {Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.210530730056432, 1.3559324389141183] <- {Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.210530730056432, 1.472494685832072] <- {Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.210530730056432, 1.3559324389141183] <- {Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.18.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{w}{x} = \pderiv[2]{w}{y}+\frac{1}{y}\pderiv{w}{y}} | diff(w, [x$(2)])= diff(w, [y$(2)])+(1)/(y)*diff(w, y) |
D[w, {x, 2}]= D[w, {y, 2}]+Divide[1,y]*D[w, y] |
Successful | Successful | - | - |
| 19.18.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{W}{t} = \pderiv[2]{W}{x}+\pderiv[2]{W}{y}} | diff(W, [t$(2)])= diff(W, [x$(2)])+ diff(W, [y$(2)]) |
D[W, {t, 2}]= D[W, {x, 2}]+ D[W, {y, 2}] |
Successful | Successful | - | - |
| 19.18.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{u}{x}+\pderiv[2]{u}{y}+\frac{1}{y}\pderiv{u}{y} = 0} | diff(u, [x$(2)])+ diff(u, [y$(2)])+(1)/(y)*diff(u, y)= 0 |
D[u, {x, 2}]+ D[u, {y, 2}]+Divide[1,y]*D[u, y]= 0 |
Successful | Successful | - | - |
| 19.18.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{U}{x}+\pderiv[2]{U}{y}+\pderiv[2]{U}{z} = 0} | diff(U, [x$(2)])+ diff(U, [y$(2)])+ diff(U, [z$(2)])= 0 |
D[U, {x, 2}]+ D[U, {y, 2}]+ D[U, {z, 2}]= 0 |
Successful | Successful | - | - |
| 19.20#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{x}{x} = x^{-1/2}} | 0.5*int(1/(sqrt(t+x)*sqrt(t+x)*sqrt(t+x)), t = 0..infinity)= (x)^(- 1/ 2) |
Error |
Error | Error | - | - |
| 19.20#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{\lambda x}{\lambda y}{\lambda z} = \lambda^{-1/2}\CarlsonsymellintRF@{x}{y}{z}} | 0.5*int(1/(sqrt(t+lambda*x)*sqrt(t+lambda*y)*sqrt(t+lambda*z)), t = 0..infinity)= (lambda)^(- 1/ 2)* 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+z)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.20#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{0}{y}{y} = \tfrac{1}{2}\pi y^{-1/2}} | 0.5*int(1/(sqrt(t+0)*sqrt(t+y)*sqrt(t+y)), t = 0..infinity)=(1)/(2)*Pi*(y)^(- 1/ 2) |
Error |
Error | Error | - | - |
| 19.20#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{0}{0}{z} = \infty} | 0.5*int(1/(sqrt(t+0)*sqrt(t+0)*sqrt(t+z)), t = 0..infinity)= infinity |
Error |
Error | Error | - | - |
| 19.20.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}\frac{\diff{t}}{\sqrt{1-t^{4}}} = \CarlsonsymellintRF@{0}{1}{2}} | int((1)/(sqrt(1 - (t)^(4))), t = 0..1)= 0.5*int(1/(sqrt(t+0)*sqrt(t+1)*sqrt(t+2)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.20.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{0}{1}{2} = \frac{\left(\EulerGamma@{\frac{1}{4}}\right)^{2}}{4(2\pi)^{1/2}}} | 0.5*int(1/(sqrt(t+0)*sqrt(t+1)*sqrt(t+2)), t = 0..infinity)=((GAMMA((1)/(4)))^(2))/(4*(2*Pi)^(1/ 2)) |
Error |
Error | Error | - | - |
| 19.21.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{0}{z-1}{z} = \CarlsonsymellintRF@{0}{1-z}{1}-\iunit\!\CarlsonsymellintRF@{0}{z}{1}} | 0.5*int(1/(sqrt(t+0)*sqrt(t+z - 1)*sqrt(t+z)), t = 0..infinity)= 0.5*int(1/(sqrt(t+0)*sqrt(t+1 - z)*sqrt(t+1)), t = 0..infinity)- I*0.5*int(1/(sqrt(t+0)*sqrt(t+z)*sqrt(t+1)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.21.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{0}{z-1}{z} = \CarlsonsymellintRF@{0}{1-z}{1}+\iunit\!\CarlsonsymellintRF@{0}{z}{1}} | 0.5*int(1/(sqrt(t+0)*sqrt(t+z - 1)*sqrt(t+z)), t = 0..infinity)= 0.5*int(1/(sqrt(t+0)*sqrt(t+1 - z)*sqrt(t+1)), t = 0..infinity)+ I*0.5*int(1/(sqrt(t+0)*sqrt(t+z)*sqrt(t+1)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 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}}} | 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) |
Error |
Error | 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}}}} | 0.5*int(1/(sqrt(t+0)*sqrt(t+a(a[0])^(2))*sqrt(t+g(g[0])^(2))), t = 0..infinity)=(1)/(GaussAGM(a[0], g[0])) |
Error |
Error | Error | - | - |
| 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)} | (a(a[0])^(2)- sum((2)^(n - 1)* c(c[n])^(2), n = 0..infinity))(a(a[1])^(2)- sum((2)^(n - 1)* c(c[n])^(2), n = 2..infinity)) |
Error |
Failure | Error | Skip | - |
| 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}}} | 0.5*int(1/(sqrt(t+(a)^(2))*sqrt(t+z(z[-])^(2))*sqrt(t+z(z[+])^(2))), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.23.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{0}{y}{z} = \int_{0}^{\pi/2}(y\cos^{2}@@{\theta}+z\sin^{2}@@{\theta})^{-1/2}\diff{\theta}} | 0.5*int(1/(sqrt(t+0)*sqrt(t+y)*sqrt(t+z)), t = 0..infinity)= int((y*(cos(theta))^(2)+ z*(sin(theta))^(2))^(- 1/ 2), theta = 0..Pi/ 2) |
Error |
Error | Error | - | - |
| 19.23.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 4\pi\CarlsonsymellintRF@{x}{y}{z} = \int_{0}^{2\pi}\!\!\!\!\int_{0}^{\pi}\frac{\sin@@{\theta}\diff{\theta}\diff{\phi}}{(x\sin^{2}@@{\theta}\cos^{2}@@{\phi}+y\sin^{2}@@{\theta}\sin^{2}@@{\phi}+z\cos^{2}@@{\theta})^{1/2}}} | 4*Pi*0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+z)), t = 0..infinity)= int(int((sin(theta))/((x*(sin(theta))^(2)* (cos(phi))^(2)+ y*(sin(theta))^(2)* (sin(phi))^(2)+ z*(cos(theta))^(2))^(1/ 2)), theta = 0..Pi), phi = 0..2*Pi) |
Error |
Error | Error | - | - |
| 19.24.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{a_{n}} <= \frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}}} | (1)/(a[n])< 0.5*int(1/(sqrt(t+0)*sqrt(t+a(a[0])^(2))*sqrt(t+g(g[0])^(2))), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.24.E5 | 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}{g_{n}}} | 0.5*int(1/(sqrt(t+0)*sqrt(t+a(a[0])^(2))*sqrt(t+g(g[0])^(2))), t = 0..infinity)< =(1)/(g[n]) |
Error |
Error | Error | - | - |
| 19.24.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{3}{\sqrt{x}+\sqrt{y}+\sqrt{z}} <= \CarlsonsymellintRF@{x}{y}{z}} | (3)/(sqrt(x)+sqrt(y)+sqrt(z))< = 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+z)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.24.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{z} <= \frac{1}{(xyz)^{1/6}}} | 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+z)), t = 0..infinity)< =(1)/((x*y*z)^(1/ 6)) |
Error |
Error | Error | - | - |
| 19.25#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = \CarlsonsymellintRF@{0}{{k^{\prime}}^{2}}{1}} | EllipticK(k)= 0.5*int(1/(sqrt(t+0)*sqrt(t+1 - (k)^(2))*sqrt(t+1)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.25#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k}-\compellintEk@{k} = k^{2}\compellintDk@{k}} | EllipticK(k)- EllipticE(k)= (k)^(2)* (EllipticK(k) - EllipticE(k))/(k)^2 |
EllipticK[(k)^2]- EllipticE[(k)^2]= (k)^(2)* Divide[EllipticK[(k)^2] - EllipticE[(k)^2], (k)^4] |
Successful | Failure | - | Fail
Complex[0.3274322182097533, -1.81658404135269] <- {Rule[k, 2]}Complex[0.24314000376678657, -2.9699762712345015] <- {Rule[k, 3]} |
| 19.25.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{k} = \CarlsonsymellintRF@{c-1}{c-k^{2}}{c}} | EllipticF(sin(phi), k)= 0.5*int(1/(sqrt(t+c - 1)*sqrt(t+c - (k)^(2))*sqrt(t+c)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.25.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{k} = \CarlsonsymellintRF@{x}{y}{z}} | EllipticF(sin(phi), k)= 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+z)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.25.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z-x)^{1/2}\CarlsonsymellintRF@{x}{y}{z} = \incellintFk@{\phi}{k}} | (z - x)^(1/ 2)* 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+z)), t = 0..infinity)= EllipticF(sin(phi), k) |
Error |
Error | Error | - | - |
| 19.25.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u = \CarlsonsymellintRF@{\genJacobiellk{p}{s}^{2}@{u}{k}}{\genJacobiellk{q}{s}^{2}@{u}{k}}{\genJacobiellk{r}{s}^{2}@{u}{k}}} | u = 0.5*int(1/(sqrt(t+genJacobiellk(p)*(s)^(2)* u*k)*sqrt(t+genJacobiellk(q)*(s)^(2)* u*k)*sqrt(t+genJacobiellk(r)*(s)^(2)* u*k)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.26.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x+\lambda}{y+\lambda}{z+\lambda}+\CarlsonsymellintRF@{x+\mu}{y+\mu}{z+\mu} = \CarlsonsymellintRF@{x}{y}{z}} | 0.5*int(1/(sqrt(t+x + lambda)*sqrt(t+y + lambda)*sqrt(t+z + lambda)), t = 0..infinity)+ 0.5*int(1/(sqrt(t+x + mu)*sqrt(t+y + mu)*sqrt(t+z + mu)), t = 0..infinity)= 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+z)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.26.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{\lambda}{y+\lambda}{z+\lambda} = {\CarlsonsymellintRF@{0}{y}{z}-\CarlsonsymellintRF@{\mu}{y+\mu}{z+\mu},}} | 0.5*int(1/(sqrt(t+lambda)*sqrt(t+y + lambda)*sqrt(t+z + lambda)), t = 0..infinity)=0.5*int(1/(sqrt(t+0)*sqrt(t+y)*sqrt(t+z)), t = 0..infinity)- 0.5*int(1/(sqrt(t+mu)*sqrt(t+y + mu)*sqrt(t+z + mu)), t = 0..infinity), |
Error |
Error | Error | - | - |
| 19.26.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{z} = 2\!\CarlsonsymellintRF@{x+\lambda}{y+\lambda}{z+\lambda}} | 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+z)), t = 0..infinity)= 2*0.5*int(1/(sqrt(t+x + lambda)*sqrt(t+y + lambda)*sqrt(t+z + lambda)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.26.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\!\CarlsonsymellintRF@{x+\lambda}{y+\lambda}{z+\lambda} = \CarlsonsymellintRF@{\frac{x+\lambda}{4}}{\frac{y+\lambda}{4}}{\frac{z+\lambda}{4}}} | 2*0.5*int(1/(sqrt(t+x + lambda)*sqrt(t+y + lambda)*sqrt(t+z + lambda)), t = 0..infinity)= 0.5*int(1/(sqrt(t+(x + lambda)/(4))*sqrt(t+(y + lambda)/(4))*sqrt(t+(z + lambda)/(4))), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.28.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}t^{\sigma-1}\CarlsonsymellintRF@{0}{t}{1}\diff{t} = \tfrac{1}{2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}} | int((t)^(sigma - 1)* 0.5*int(1/(sqrt(t+0)*sqrt(t+t)*sqrt(t+1)), t = 0..infinity), t = 0..1)=(1)/(2)*(Beta(sigma, (1)/(2)))^(2) |
Error |
Error | Error | - | - |
| 19.28.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi/2}\CarlsonsymellintRF@{\sin^{2}@@{\theta}\cos^{2}@{x+y}}{\sin^{2}@@{\theta}\cos^{2}@{x-y}}{1}\diff{\theta} = \CarlsonsymellintRF@{0}{\cos^{2}@@{x}}{1}\CarlsonsymellintRF@{0}{\cos^{2}@@{y}}{1}} | int(0.5*int(1/(sqrt(t+(sin(theta))^(2)* (cos(x + y))^(2))*sqrt(t+(sin(theta))^(2)* (cos(x - y))^(2))*sqrt(t+1)), t = 0..infinity), theta = 0..Pi/ 2)= 0.5*int(1/(sqrt(t+0)*sqrt(t+(cos(x))^(2))*sqrt(t+1)), t = 0..infinity)*0.5*int(1/(sqrt(t+0)*sqrt(t+(cos(y))^(2))*sqrt(t+1)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.29.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{s(t)} = 2\!\CarlsonsymellintRF@{U_{12}^{2}}{U_{13}^{2}}{U_{23}^{2}}} | 0.5*int(1/(sqrt(t+U(U[12])^(2))*sqrt(t+U(U[13])^(2))*sqrt(t+U(U[23])^(2))), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.29.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle I(\mathbf{m}) = \int_{y}^{x}\prod_{\alpha=1}^{h}(a_{\alpha}+b_{\alpha}t)^{-1/2}\prod_{j=1}^{n}(a_{j}+b_{j}t)^{m_{j}}\diff{t}} | I*(m)= int(product((a[alpha]+ b[alpha]*t)^(- 1/ 2)* product((a[j]+ b[j]*t)^(m[j]), j = 1..n), alpha = 1..h), t = y..x) |
I*(m)= Integrate[Product[(Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*t)^(- 1/ 2)* Product[(Subscript[a, j]+ Subscript[b, j]*t)^(Subscript[m, j]), {j, 1, n}], {\[Alpha], 1, h}], {t, y, x}] |
Error | Failure | - | Error |
| 19.29.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{j}^{q}I(q\mathbf{e}_{l}) = \sum_{r=0}^{q}\binom{q}{r}b_{l}^{r}d_{lj}^{q-r}I(r\mathbf{e}_{j})} | (b[j])^(q)*I*sum(binomial(q,r)*b(b[l])^(r)*d(d[l*j])^(q - r)*I*(r*e[j]), r = 0..q) |
(Subscript[b, j])^(q)*I*Sum[Binomial[q,r]*b(Subscript[b, l])^(r)*d(Subscript[d, l*j])^(q - r)*I*(r*Subscript[e, j]), {r, 0, q}] |
Failure | Failure | Skip | Error |
| 19.29.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{\sqrt{Q_{1}(t)Q_{2}(t)}} = \CarlsonsymellintRF@{U^{2}+a_{1}b_{2}}{U^{2}+a_{2}b_{1}}{U^{2}}} | int((1)/(sqrt(Q[1]*(t)* Q[2]*(t))), t = y..x)= 0.5*int(1/(sqrt(t+(U)^(2)+ a[1]*b[2])*sqrt(t+(U)^(2)+ a[2]*b[1])*sqrt(t+(U)^(2))), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.29.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{\infty}\frac{\diff{t}}{\sqrt{(t^{2}+a^{2})(t^{2}-b^{2})}} = \CarlsonsymellintRF@{y^{2}+a^{2}}{y^{2}-b^{2}}{y^{2}}} | int((1)/(sqrt(((t)^(2)+ (a)^(2))*((t)^(2)- (b)^(2)))), t = y..infinity)= 0.5*int(1/(sqrt(t+(y)^(2)+ (a)^(2))*sqrt(t+(y)^(2)- (b)^(2))*sqrt(t+(y)^(2))), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.29.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{\sqrt{Q_{1}(t)Q_{2}(t)}} = 4\!\CarlsonsymellintRF@{U}{U+D_{12}+V}{U+D_{12}-V}} | int((1)/(sqrt(Q[1]*(t)* Q[2]*(t))), t = y..x)= 4*0.5*int(1/(sqrt(t+U)*sqrt(t+U + D[12]+ V)*sqrt(t+U + D[12]- V)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.29.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{\sqrt{t^{3}-a^{3}}} = 4\!\CarlsonsymellintRF@{U}{U-3a+2\sqrt{3}a}{U-3a-2\sqrt{3}a}} | int((1)/(sqrt((t)^(3)- (a)^(3))), t = y..x)= 4*0.5*int(1/(sqrt(t+U)*sqrt(t+U - 3*a + 2*sqrt(3)*a)*sqrt(t+U - 3*a - 2*sqrt(3)*a)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.29.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{\sqrt{Q(t^{2})}} = 2\!\CarlsonsymellintRF@{U}{U-g+2\sqrt{fh}}{U-g-2\sqrt{fh}}} | int((1)/(sqrt(Q*((t)^(2)))), t = y..x)= 2*0.5*int(1/(sqrt(t+U)*sqrt(t+U - g + 2*sqrt(f*h))*sqrt(t+U - g - 2*sqrt(f*h))), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.29.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{\sqrt{t^{4}+a^{4}}} = 2\!\CarlsonsymellintRF@{U}{U+2a^{2}}{U-2a^{2}}} | int((1)/(sqrt((t)^(4)+ (a)^(4))), t = y..x)= 2*0.5*int(1/(sqrt(t+U)*sqrt(t+U + 2*(a)^(2))*sqrt(t+U - 2*(a)^(2))), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.30#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = a\sin@@{\phi}} | x = a*sin(phi) |
x = a*Sin[\[Phi]] |
Failure | Failure | Fail -1.615975576-3.469485904*I <- {a = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), x = 1}-.615975576-3.469485904*I <- {a = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), x = 2}.384024424-3.469485904*I <- {a = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), x = 3}-2.469485904-2.615975576*I <- {a = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Skip |
| 19.30#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = b\cos@@{\phi}} | y = b*cos(phi) |
y = b*Cos[\[Phi]] |
Failure | Failure | Fail -2.183489624+2.222746490*I <- {b = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), y = 1}-1.183489624+2.222746490*I <- {b = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), y = 2}-.183489624+2.222746490*I <- {b = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), y = 3}3.222746490-3.183489624*I <- {b = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)-I*2^(1/2), y = 1}... skip entries to safe data |
Fail
Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.2227464935806323, -3.183489625260803] <- {Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.30.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s = a\int_{0}^{\phi}\sqrt{1-k^{2}\sin^{2}@@{\theta}}\diff{\theta}} | s = a*int(sqrt(1 - (k)^(2)* (sin(theta))^(2)), theta = 0..phi) |
s = a*Integrate[Sqrt[1 - (k)^(2)* (Sin[\[Theta]])^(2)], {\[Theta], 0, \[Phi]}] |
Failure | Failure | Skip | Error |
| 19.30.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s/a = \incellintEk@{\phi}{k}} | s/ a = EllipticE(sin(phi), k) |
s/ a = EllipticE[\[Phi], (k)^2] |
Failure | Failure | Fail -1.151535540-.3017614705*I <- {a = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), s = 2^(1/2)+I*2^(1/2), k = 1}-2.941278291+.6826717339*I <- {a = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), s = 2^(1/2)+I*2^(1/2), k = 2}-4.812988572+1.491347909*I <- {a = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), s = 2^(1/2)+I*2^(1/2), k = 3}-2.151535540-1.301761470*I <- {a = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), s = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Skip |
| 19.30#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c = \csc^{2}@@{\phi}} | c = (csc(phi))^(2) |
c = (Csc[\[Phi]])^(2) |
Failure | Failure | Fail 1.210530730+1.472494686*I <- {c = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2)}1.210530730+1.355932438*I <- {c = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)-I*2^(1/2)}1.210530730+1.472494686*I <- {c = 2^(1/2)+I*2^(1/2), phi = -2^(1/2)-I*2^(1/2)}1.210530730+1.355932438*I <- {c = 2^(1/2)+I*2^(1/2), phi = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.210530730056432, 1.472494685832072] <- {Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.210530730056432, 1.3559324389141183] <- {Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.210530730056432, 1.472494685832072] <- {Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.210530730056432, 1.3559324389141183] <- {Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.30.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L(a,b) = 4a\compellintEk@{k}} | L*(a , b)= 4*a*EllipticE(k) |
L*(a , b)= 4*a*EllipticE[(k)^2] |
Failure | Failure | Error | Error |
| 19.30.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{s}{(1/k)} = \sqrt{a^{2}-b^{2}}\incellintFk@{\phi}{k}} | diff(s, 1/ k)=sqrt((a)^(2)- (b)^(2))*EllipticF(sin(phi), k) |
D[s, 1/ k]=Sqrt[(a)^(2)- (b)^(2)]*EllipticF[\[Phi], (k)^2] |
Error | Failure | - | Successful |
| 19.30.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{a^{2}-b^{2}}\incellintFk@{\phi}{k} = \sqrt{a^{2}-b^{2}}\CarlsonsymellintRF@{c-1}{c-k^{2}}{c}} | sqrt((a)^(2)- (b)^(2))*EllipticF(sin(phi), k)=sqrt((a)^(2)- (b)^(2))*0.5*int(1/(sqrt(t+c - 1)*sqrt(t+c - (k)^(2))*sqrt(t+c)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.30.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s = \frac{1}{2}\int_{0}^{y^{2}/b^{2}}\sqrt{\frac{(a^{2}+b^{2})t+b^{2}}{t(t+1)}}\diff{t}} | s =(1)/(2)*int(sqrt((((a)^(2)+ (b)^(2))* t + (b)^(2))/(t*(t + 1))), t = 0..(y)^(2)/ (b)^(2)) |
s =Divide[1,2]*Integrate[Sqrt[Divide[((a)^(2)+ (b)^(2))* t + (b)^(2),t*(t + 1)]], {t, 0, (y)^(2)/ (b)^(2)}] |
Failure | Failure | Skip | Error |
| 19.30.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s = \tfrac{1}{2}I(\mathbf{e}_{1})} | s =(1)/(2)*I*(e[1]) |
s =Divide[1,2]*I*(Subscript[e, 1]) |
Failure | Failure | Skip | Successful |
| 19.30.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r^{2} = 2a^{2}\cos@{2\theta}} | (r)^(2)= 2*(a)^(2)* cos(2*theta) |
(r)^(2)= 2*(a)^(2)* Cos[2*\[Theta]] |
Failure | Failure | Skip | Successful |
| 19.30.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s = 2a^{2}\int_{0}^{r}\frac{\diff{t}}{\sqrt{4a^{4}-t^{4}}}} | s = 2*(a)^(2)* int((1)/(sqrt(4*(a)^(4)- (t)^(4))), t = 0..r) |
s = 2*(a)^(2)* Integrate[Divide[1,Sqrt[4*(a)^(4)- (t)^(4)]], {t, 0, r}] |
Error | Failure | - | Error |
| 19.30.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2a^{2}\int_{0}^{r}\frac{\diff{t}}{\sqrt{4a^{4}-t^{4}}} = \sqrt{2a^{2}}\CarlsonsymellintRF@{q-1}{q}{q+1}} | 2*(a)^(2)* int((1)/(sqrt(4*(a)^(4)- (t)^(4))), t = 0..r)=sqrt(2*(a)^(2))*0.5*int(1/(sqrt(t+q - 1)*sqrt(t+q)*sqrt(t+q + 1)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.30.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s = a\incellintFk@{\phi}{1/\sqrt{2}}} | s = a*EllipticF(sin(phi), 1/sqrt(2)) |
s = a*EllipticF[\[Phi], (1/Sqrt[2])^2] |
Failure | Failure | Fail 2.831268677-2.040721799*I <- {a = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), s = 2^(1/2)+I*2^(1/2)}2.831268677-4.869148923*I <- {a = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), s = 2^(1/2)-I*2^(1/2)}.2841553e-2-4.869148923*I <- {a = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), s = -2^(1/2)-I*2^(1/2)}.2841553e-2-2.040721799*I <- {a = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), s = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[2.831268678966966, -2.040721798901064] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[s, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.040721798901064, 2.831268678966966] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[s, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.0028415542207758104, 4.869148923647254] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[s, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.869148923647254, -0.0028415542207758104] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[s, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.30.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle P = 4\sqrt{2a^{2}}\CarlsonsymellintRF@{0}{1}{2}} | P = 4*sqrt(2*(a)^(2))*0.5*int(1/(sqrt(t+0)*sqrt(t+1)*sqrt(t+2)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.32.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(p) = \CarlsonsymellintRF@{p-x_{1}}{p-x_{2}}{p-x_{3}}} | z*(p)= 0.5*int(1/(sqrt(t+p - x[1])*sqrt(t+p - x[2])*sqrt(t+p - x[3])), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.32#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(x_{3}) = \CarlsonsymellintRF@{x_{3}-x_{1}}{x_{3}-x_{2}}{0}} | z*(x[3])= 0.5*int(1/(sqrt(t+x[3]- x[1])*sqrt(t+x[3]- x[2])*sqrt(t+0)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.32#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x_{3}-x_{1}}{x_{3}-x_{2}}{0} = -i\CarlsonsymellintRF@{0}{x_{1}-x_{3}}{x_{2}-x_{3}}} | 0.5*int(1/(sqrt(t+x[3]- x[1])*sqrt(t+x[3]- x[2])*sqrt(t+0)), t = 0..infinity)= - I*0.5*int(1/(sqrt(t+0)*sqrt(t+x[1]- x[3])*sqrt(t+x[2]- x[3])), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.33.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{S}{2\pi} = c^{2}+\frac{ab}{\sin@@{\phi}}\left(\incellintEk@{\phi}{k}\sin^{2}@@{\phi}+\incellintFk@{\phi}{k}\cos^{2}@@{\phi}\right)} | (S)/(2*Pi)= (c)^(2)+(a*b)/(sin(phi))*(EllipticE(sin(phi), k)*(sin(phi))^(2)+ EllipticF(sin(phi), k)*(cos(phi))^(2)) |
Divide[S,2*Pi]= (c)^(2)+Divide[a*b,Sin[\[Phi]]]*(EllipticE[\[Phi], (k)^2]*(Sin[\[Phi]])^(2)+ EllipticF[\[Phi], (k)^2]*(Cos[\[Phi]])^(2)) |
Failure | Failure | Skip | Error |
| 19.33#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\phi} = \frac{c}{a}} | cos(phi)=(c)/(a) |
Cos[\[Phi]]=Divide[c,a] |
Failure | Failure | Fail -.6603260076-1.911393109*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2)}-.6603260076+1.911393109*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)-I*2^(1/2)}-.6603260076-1.911393109*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), phi = -2^(1/2)-I*2^(1/2)}-.6603260076+1.911393109*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), phi = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[0.13599115937806153, -1.8531119867052335] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[$0, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.13599115937806153, -1.9696742336231872] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[$0, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.13599115937806153, -1.8531119867052335] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[$0, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.13599115937806153, -1.9696742336231872] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[$0, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 19.33.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle V(\lambda) = Q\CarlsonsymellintRF@{a^{2}+\lambda}{b^{2}+\lambda}{c^{2}+\lambda}} | V*(lambda)= Q*0.5*int(1/(sqrt(t+(a)^(2)+ lambda)*sqrt(t+(b)^(2)+ lambda)*sqrt(t+(c)^(2)+ lambda)), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.33.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1/C = \CarlsonsymellintRF@{a^{2}}{b^{2}}{c^{2}}} | 1/ C = 0.5*int(1/(sqrt(t+(a)^(2))*sqrt(t+(b)^(2))*sqrt(t+(c)^(2))), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.33.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L_{c} = 2\pi abc\int_{0}^{\infty}\frac{\diff{\lambda}}{\sqrt{(a^{2}+\lambda)(b^{2}+\lambda)(c^{2}+\lambda)^{3}}}} | L[c]= 2*Pi*a*b*c*int((1)/(sqrt(((a)^(2)+ lambda)*((b)^(2)+ lambda)*((c)^(2)+ lambda)^(3))), lambda = 0..infinity) |
Subscript[L, c]= 2*Pi*a*b*c*Integrate[Divide[1,Sqrt[((a)^(2)+ \[Lambda])*((b)^(2)+ \[Lambda])*((c)^(2)+ \[Lambda])^(3)]], {\[Lambda], 0, Infinity}] |
Failure | Failure | Skip | Error |
| 19.34.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle ab\int_{0}^{2\pi}(h^{2}+a^{2}+b^{2}-2ab\cos@@{\theta})^{-1/2}\cos@@{\theta}\diff{\theta} = 2ab\int_{-1}^{1}\frac{t\diff{t}}{\sqrt{(1+t)(1-t)(a_{3}-2abt)}}} | a*b*int(((h)^(2)+ (a)^(2)+ (b)^(2)- 2*a*b*cos(theta))^(- 1/ 2)* cos(theta), theta = 0..2*Pi)= 2*a*b*int((t)/(sqrt((1 + t)*(1 - t)*(a[3]- 2*a*b*t))), t = - 1..1) |
a*b*Integrate[((h)^(2)+ (a)^(2)+ (b)^(2)- 2*a*b*Cos[\[Theta]])^(- 1/ 2)* Cos[\[Theta]], {\[Theta], 0, 2*Pi}]= 2*a*b*Integrate[Divide[t,Sqrt[(1 + t)*(1 - t)*(Subscript[a, 3]- 2*a*b*t)]], {t, - 1, 1}] |
Failure | Failure | Skip | Error |
| 19.34.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2ab\int_{-1}^{1}\frac{t\diff{t}}{\sqrt{(1+t)(1-t)(a_{3}-2abt)}} = 2abI(\mathbf{e}_{5})} | 2*a*b*int((t)/(sqrt((1 + t)*(1 - t)*(a[3]- 2*a*b*t))), t = - 1..1)= 2*a*b*I*(e[5]) |
2*a*b*Integrate[Divide[t,Sqrt[(1 + t)*(1 - t)*(Subscript[a, 3]- 2*a*b*t)]], {t, - 1, 1}]= 2*a*b*I*(Subscript[e, 5]) |
Failure | Failure | Skip | Error |
| 19.36.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{1}{2}{4} = \CarlsonsymellintRF@{z_{1}}{z_{2}}{z_{3}}} | 0.5*int(1/(sqrt(t+1)*sqrt(t+2)*sqrt(t+4)), t = 0..infinity)= 0.5*int(1/(sqrt(t+z[1])*sqrt(t+z[2])*sqrt(t+z[3])), t = 0..infinity) |
Error |
Error | Error | - | - |
| 19.36.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{t_{0}^{2}}{t_{0}^{2}+\theta c_{0}^{2}}{t_{0}^{2}+\theta a_{0}^{2}} = \CarlsonsymellintRF@{T^{2}}{T^{2}}{T^{2}+\theta M^{2}}} | 0.5*int(1/(sqrt(t+t(t[0])^(2))*sqrt(t+t(t[0])^(2)+ theta*c(c[0])^(2))*sqrt(t+t(t[0])^(2)+ theta*a(a[0])^(2))), t = 0..infinity)= 0.5*int(1/(sqrt(t+(T)^(2))*sqrt(t+(T)^(2))*sqrt(t+(T)^(2)+ theta*(M)^(2))), t = 0..infinity) |
Error |
Error | Error | - | - |