Results of Elliptic Integrals I
This is the first half of the chapter Elliptic Integrals. It shows results from Section 19.1 to 19.21. For Section 19.22 to 19.36 go to Elliptic Integrals II.
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 19.2.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r(s,t) = \frac{(p_{1}+p_{2}s)(p_{3}-p_{4}s)s}{(p_{3}+p_{4}s)(p_{3}-p_{4}s)s}} | r*(s , t) = ((p[1]+ p[2]*s)*(p[3]- p[4]*s)* s)/((p[3]+ p[4]*s)*(p[3]- p[4]*s)* s) |
r*(s , t) == Divide[(Subscript[p, 1]+ Subscript[p, 2]*s)*(Subscript[p, 3]- Subscript[p, 4]*s)* s,(Subscript[p, 3]+ Subscript[p, 4]*s)*(Subscript[p, 3]- Subscript[p, 4]*s)* s] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 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]}, GenerateConditions->None] |
Failure | Aborted | Failed [6 / 30] 6/30]: [[Float(infinity) <- {phi = -2, k = 1}.2e-9-.5175477340*I <- {phi = -2, k = 2} |
Skipped - Because timed out |
| 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]}, GenerateConditions->None] == Integrate[Divide[1,Sqrt[1 - (t)^(2)]*Sqrt[1 - (k)^(2)* (t)^(2)]], {t, 0, Sin[\[Phi]]}, GenerateConditions->None] |
Failure | Aborted | Failed [6 / 30] 6/30]: [[Float(-infinity) <- {phi = -2, k = 1}-.2e-9+.5175477340*I <- {phi = -2, k = 2} |
Skipped - Because timed out |
| 19.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} = \int_{0}^{\phi}\sqrt{1-k^{2}\sin^{2}@@{\theta}}\diff{\theta}\\} | EllipticE(sin(phi), k) = int(sqrt(1 - (k)^(2)* (sin(theta))^(2)), theta = 0..phi) |
EllipticE[\[Phi], (k)^2] == Integrate[Sqrt[1 - (k)^(2)* (Sin[\[Theta]])^(2)], {\[Theta], 0, \[Phi]}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 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]}, GenerateConditions->None] == Integrate[Divide[Sqrt[1 - (k)^(2)* (t)^(2)],Sqrt[1 - (t)^(2)]], {t, 0, Sin[\[Phi]]}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 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]}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 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]}, GenerateConditions->None] == Integrate[Divide[(t)^(2),Sqrt[1 - (t)^(2)]*Sqrt[1 - (k)^(2)* (t)^(2)]], {t, 0, Sin[\[Phi]]}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 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]]}, GenerateConditions->None] == (EllipticF[\[Phi], (k)^2]- EllipticE[\[Phi], (k)^2])/ (k)^(2) |
Failure | Aborted | Successful [Tested: 0] | Skipped - Because timed out |
| 19.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{\alpha^{2}}{k} = \int_{0}^{\phi}\frac{\diff{\theta}}{\sqrt{1-k^{2}\sin^{2}@@{\theta}}(1-\alpha^{2}\sin^{2}@@{\theta})}} | EllipticPi(sin(phi), (alpha)^(2), k) = int((1)/(sqrt(1 - (k)^(2)* (sin(theta))^(2))*(1 - (alpha)^(2)* (sin(theta))^(2))), theta = 0..phi) |
EllipticPi[\[Alpha]^(2), \[Phi],(k)^2] == Integrate[Divide[1,Sqrt[1 - (k)^(2)* (Sin[\[Theta]])^(2)]*(1 - \[Alpha]^(2)* (Sin[\[Theta]])^(2))], {\[Theta], 0, \[Phi]}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.2.E7 | 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}}(1-\alpha^{2}\sin^{2}@@{\theta})} = \int_{0}^{\sin@@{\phi}}\frac{\diff{t}}{\sqrt{1-t^{2}}\sqrt{1-k^{2}t^{2}}(1-\alpha^{2}t^{2})}} | int((1)/(sqrt(1 - (k)^(2)* (sin(theta))^(2))*(1 - (alpha)^(2)* (sin(theta))^(2))), theta = 0..phi) = int((1)/(sqrt(1 - (t)^(2))*sqrt(1 - (k)^(2)* (t)^(2))*(1 - (alpha)^(2)* (t)^(2))), t = 0..sin(phi)) |
Integrate[Divide[1,Sqrt[1 - (k)^(2)* (Sin[\[Theta]])^(2)]*(1 - \[Alpha]^(2)* (Sin[\[Theta]])^(2))], {\[Theta], 0, \[Phi]}, GenerateConditions->None] == Integrate[Divide[1,Sqrt[1 - (t)^(2)]*Sqrt[1 - (k)^(2)* (t)^(2)]*(1 - \[Alpha]^(2)* (t)^(2))], {t, 0, Sin[\[Phi]]}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 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 | - | Successful [Tested: 3] |
| 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 | - | Successful [Tested: 3] |
| 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 | - | Successful [Tested: 3] |
| 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 | - | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]}Complex[-0.08185805455243832, 0.4541460103381725] <- {Rule[k, 2]} |
| 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 | - | Successful [Tested: 9] |
| 19.2#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ccompellintKk@{k} = \compellintKk@{k^{\prime}}} | EllipticCK(k) = EllipticK(sqrt(1 - (k)^(2))) |
EllipticK[1-(k)^2] == EllipticK[(Sqrt[1 - (k)^(2)])^2] |
Successful | Successful | - | Successful [Tested: 3] |
| 19.2#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ccompellintEk@{k} = \compellintEk@{k^{\prime}}} | EllipticCE(k) = EllipticE(sqrt(1 - (k)^(2))) |
EllipticE[1-(k)^2] == EllipticE[(Sqrt[1 - (k)^(2)])^2] |
Successful | Successful | - | Successful [Tested: 3] |
| 19.2#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{\prime} = \sqrt{1-k^{2}}} | sqrt(1 - (k)^(2)) = sqrt(1 - (k)^(2)) |
Sqrt[1 - (k)^(2)] == Sqrt[1 - (k)^(2)] |
Successful | Successful | - | Successful [Tested: 3] |
| 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 | Failed [30 / 90]
{Indeterminate <- {Rule[k, 1], Rule[m, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Indeterminate <- {Rule[k, 1], Rule[m, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [30 / 90]
{Indeterminate <- {Rule[k, 1], Rule[m, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Indeterminate <- {Rule[k, 1], Rule[m, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [90 / 90] 90/90]: [[-3.717960670-.6751929261*I <- {phi = 1/2*3^(1/2)+1/2*I, k = 1, m = 1}-4.000000000-.3e-9*I <- {phi = 1/2*3^(1/2)+1/2*I, k = 1, m = 2} |
Successful [Tested: 90] |
| 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 | Failed [90 / 90] 90/90]: [[-.2820393315+.6751929264*I <- {phi = 1/2*3^(1/2)+1/2*I, k = 1, m = 1}-4.000000000-.4e-9*I <- {phi = 1/2*3^(1/2)+1/2*I, k = 1, m = 2} |
Successful [Tested: 90] |
| 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 | Failed [30 / 90]
{Indeterminate <- {Rule[k, 1], Rule[m, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Indeterminate <- {Rule[k, 1], Rule[m, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [30 / 90]
{Indeterminate <- {Rule[k, 1], Rule[m, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Indeterminate <- {Rule[k, 1], Rule[m, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.2.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\atan@@{x}}\frac{\diff{\theta}}{(\cos^{2}@@{\theta}+p\sin^{2}@@{\theta})\sqrt{\cos^{2}@@{\theta}+k_{c}^{2}\sin^{2}@@{\theta}}} = \incellintPik@{\atan@@{x}}{1-p}{k}} | int((1)/(((cos(theta))^(2)+ p*(sin(theta))^(2))*sqrt((cos(theta))^(2)+ k(k[c])^(2)*(sin(theta))^(2))), theta = 0..arctan(x)) = EllipticPi(sin(arctan(x)), 1 - p, k) |
Integrate[Divide[1,((Cos[\[Theta]])^(2)+ p*(Sin[\[Theta]])^(2))*Sqrt[(Cos[\[Theta]])^(2)+ k(Subscript[k, c])^(2)*(Sin[\[Theta]])^(2)]], {\[Theta], 0, ArcTan[x]}, GenerateConditions->None] == EllipticPi[1 - p, ArcTan[x],(k)^2] |
Error | Aborted | - | Skipped - Because timed out |
| 19.2.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x}{y} = \frac{1}{2}\int_{0}^{\infty}\frac{\diff{t}}{\sqrt{t+x}(t+y)}} | Error |
1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)] == Divide[1,2]*Integrate[Divide[1,Sqrt[t + x]*(t + y)], {t, 0, Infinity}, GenerateConditions->None] |
Missing Macro Error | Failure | - | Failed [12 / 18]
{Complex[-1.0177225554447185, 0.0] <- {Rule[x, 1.5], Rule[y, -1.5]}Indeterminate <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.2.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x}{y} = \frac{1}{\sqrt{y-x}}\atan@@{\sqrt{\frac{y-x}{x}}}} | Error |
1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)] == Divide[1,Sqrt[y - x]]*ArcTan[Sqrt[Divide[y - x,x]]] |
Missing Macro Error | Failure | Skip - symbolical successful subtest | Successful [Tested: 3] |
| 19.2.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\sqrt{y-x}}\atan@@{\sqrt{\frac{y-x}{x}}} = \frac{1}{\sqrt{y-x}}\acos@@{\sqrt{x/y}}} | (1)/(sqrt(y - x))*arctan(sqrt((y - x)/(x))) = (1)/(sqrt(y - x))*arccos(sqrt(x/ y)) |
Divide[1,Sqrt[y - x]]*ArcTan[Sqrt[Divide[y - x,x]]] == Divide[1,Sqrt[y - x]]*ArcCos[Sqrt[x/ y]] |
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 19.2.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x}{y} = \frac{1}{\sqrt{x-y}}\atanh@@{\sqrt{\frac{x-y}{x}}}} | Error |
1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)] == Divide[1,Sqrt[x - y]]*ArcTanh[Sqrt[Divide[x - y,x]]] |
Missing Macro Error | Failure | Skip - symbolical successful subtest | Successful [Tested: 3] |
| 19.2.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\sqrt{x-y}}\atanh@@{\sqrt{\frac{x-y}{x}}} = \frac{1}{\sqrt{x-y}}\ln@@{\frac{\sqrt{x}+\sqrt{x-y}}{\sqrt{y}}}} | (1)/(sqrt(x - y))*arctanh(sqrt((x - y)/(x))) = (1)/(sqrt(x - y))*ln((sqrt(x)+sqrt(x - y))/(sqrt(y))) |
Divide[1,Sqrt[x - y]]*ArcTanh[Sqrt[Divide[x - y,x]]] == Divide[1,Sqrt[x - y]]*Log[Divide[Sqrt[x]+Sqrt[x - y],Sqrt[y]]] |
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 19.2.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x}{y} = \sqrt{\frac{x}{x-y}}\CarlsonellintRC@{x-y}{-y}} | Error |
1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)] == Sqrt[Divide[x,x - y]]*1/Sqrt[- y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x - y)/(- y)] |
Missing Macro Error | Failure | Skip - symbolical successful subtest | Failed [9 / 9]
{Complex[-1.0177225554447187, -0.906899682117109] <- {Rule[x, 1.5], Rule[y, -1.5]}Complex[-1.862459718905424, -1.1107207345395915] <- {Rule[x, 1.5], Rule[y, -0.5]} |
| 19.2.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\frac{x}{x-y}}\CarlsonellintRC@{x-y}{-y} = \frac{1}{\sqrt{x-y}}\atanh@@{\sqrt{\frac{x}{x-y}}}} | Error |
Sqrt[Divide[x,x - y]]*1/Sqrt[- y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x - y)/(- y)] == Divide[1,Sqrt[x - y]]*ArcTanh[Sqrt[Divide[x,x - y]]] |
Missing Macro Error | Failure | Skip - symbolical successful subtest | Successful [Tested: 9] |
| 19.2.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\sqrt{x-y}}\atanh@@{\sqrt{\frac{x}{x-y}}} = \frac{1}{\sqrt{x-y}}\ln@@{\frac{\sqrt{x}+\sqrt{x-y}}{\sqrt{-y}}}} | (1)/(sqrt(x - y))*arctanh(sqrt((x)/(x - y))) = (1)/(sqrt(x - y))*ln((sqrt(x)+sqrt(x - y))/(sqrt(- y))) |
Divide[1,Sqrt[x - y]]*ArcTanh[Sqrt[Divide[x,x - y]]] == Divide[1,Sqrt[x - y]]*Log[Divide[Sqrt[x]+Sqrt[x - y],Sqrt[- y]]] |
Failure | Failure | Successful [Tested: 9] | Successful [Tested: 9] |
| 19.2.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x}{y} = \int_{0}^{1}(v^{2}x+(1-v^{2})y)^{-1/2}\diff{v}} | Error |
1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)] == Integrate[((v)^(2)* x +(1 - (v)^(2))*y)^(- 1/ 2), {v, 0, 1}, GenerateConditions->None] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.2.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x}{y} = \frac{2}{\pi}\int_{0}^{\pi/2}\CarlsonellintRC@{y}{x\cos^{2}@@{\theta}+y\sin^{2}@@{\theta}}\diff{\theta}} | Error |
1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)] == Divide[2,Pi]*Integrate[1/Sqrt[x*(Cos[\[Theta]])^(2)+ y*(Sin[\[Theta]])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(y)/(x*(Cos[\[Theta]])^(2)+ y*(Sin[\[Theta]])^(2))], {\[Theta], 0, Pi/ 2}, GenerateConditions->None] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 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 | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]}Complex[-2.4717549813624253, 3.1435959698369205] <- {Rule[k, 2]} |
| 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 | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]}Complex[-3.3189229307917216, 6.419990143492479] <- {Rule[k, 2]} |
| 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 | - | Successful [Tested: 3] |
| 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 | - | Failed [1 / 3]
{Indeterminate <- {Rule[k, 1]} |
| 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 | - | Failed [1 / 3]
{Indeterminate <- {Rule[k, 1]} |
| 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 | - | Failed [3 / 3]
{DirectedInfinity[] <- {Rule[k, 1]}DirectedInfinity[] <- {Rule[k, 2]} |
| 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 | Failed [9 / 9]
{Indeterminate <- {Rule[k, 1], Rule[α, 1.5]}Complex[0.38994760629924174, 1.2322724929931343] <- {Rule[k, 2], Rule[α, 1.5]} |
| 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 | Failed [30 / 30] 30/30]: [[Float(infinity)+Float(infinity)*I <- {phi = 1/2*3^(1/2)+1/2*I, k = 1}-1.296981010-1.781988683*I <- {phi = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [30 / 30]
{Indeterminate <- {Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.2927667883728842, -0.7915995039632082] <- {Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | - | Successful [Tested: 30] |
| 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 | Aborted | Failed [90 / 90] 90/90]: [[Float(undefined)+Float(undefined)*I <- {alpha = 3/2, phi = 1/2*3^(1/2)+1/2*I, k = 1}-5.135398794+1.052011331*I <- {alpha = 3/2, phi = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [90 / 90]
{Indeterminate <- {Rule[k, 1], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.1264235284707635, -0.9763567309038728] <- {Rule[k, 2], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | - | Failed [300 / 300]
{Plus[Complex[0.4174282354972822, 0.36074991075375373], Times[Complex[0.43180375739814203, 0.27142936483528934], Plus[Complex[-0.8660254037844387, -0.49999999999999994], Times[Complex[-0.12500000000000003, -0.21650635094610965], D]]]] <- {Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[D, k], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Plus[Complex[-0.38000132033999284, 0.977947559972491], Times[Complex[0.3965687056216178, 0.33175091278780894], Plus[Complex[-4.763139720814413, -2.7499999999999996], Times[Complex[-0.5000000000000001, -0.8660254037844386], D]]]] <- {Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[D, k], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | - | Failed [300 / 300]
{Plus[Complex[-0.4327885168580316, -0.2292976446734403], Times[Complex[0.43278851685803155, 0.22929764467344024], Plus[Complex[2.566987298107781, -0.24999999999999997], Times[Complex[-0.12500000000000003, -0.21650635094610965], D]]]] <- {Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[D, k], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Plus[Complex[-0.6011783848834926, -0.7526006723022071], Times[Complex[0.44208095936294645, 0.16535187593702125], Plus[Complex[3.2679491924311224, -0.9999999999999999], Times[Complex[-0.5000000000000001, -0.8660254037844386], D]]]] <- {Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[D, k], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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}, GenerateConditions->None] |
Failure | Successful | Error | Successful [Tested: 3] |
| 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}, GenerateConditions->None] == Divide[Pi,2]*HypergeometricPFQ[{Divide[1,2],Divide[1,2]}, {1}, (k)^(2)] |
Failure | Successful | Failed [3 / 3] 3/3]: [[Float(infinity)+Float(infinity)*I <- {k = 1}Float(infinity)+1.078257824*I <- {k = 2} |
Successful [Tested: 3] |
| 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}, GenerateConditions->None] |
Failure | Successful | Failed [2 / 3] 2/3]: [[Float(infinity)+1.343854231*I <- {k = 2}Float(infinity)+2.498348128*I <- {k = 3} |
Successful [Tested: 3] |
| 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}, GenerateConditions->None] == Divide[Pi,2]*HypergeometricPFQ[{-Divide[1,2],Divide[1,2]}, {1}, (k)^(2)] |
Failure | Successful | Failed [2 / 3] 2/3]: [[Float(-infinity)-1.343854232*I <- {k = 2}Float(-infinity)-2.498348127*I <- {k = 3} |
Successful [Tested: 3] |
| 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}, GenerateConditions->None] |
Failure | Failure | Error | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]}Complex[-0.08185805455243848, 0.4541460103381727] <- {Rule[k, 2]} |
| 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}, GenerateConditions->None] == Divide[Pi,4]*HypergeometricPFQ[{Divide[3,2],Divide[1,2]}, {2}, (k)^(2)] |
Failure | Successful | Failed [3 / 3] 3/3]: [[Float(infinity)+Float(infinity)*I <- {k = 1}Float(infinity)+.6055280139*I <- {k = 2} |
Failed [1 / 3]
{Indeterminate <- {Rule[k, 1]} |
| 19.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintPik@{\alpha^{2}}{k} = \frac{\pi}{2}\sum_{n=0}^{\infty}\frac{\Pochhammersym{\tfrac{1}{2}}{n}}{n!}\sum_{m=0}^{n}\frac{\Pochhammersym{\tfrac{1}{2}}{m}}{m!}k^{2m}\alpha^{2n-2m}} | EllipticPi((alpha)^(2), k) = (Pi)/(2)*sum((pochhammer((1)/(2), n))/(factorial(n))*sum((pochhammer((1)/(2), m))/(factorial(m))*(k)^(2*m)* (alpha)^(2*n - 2*m), m = 0..n), n = 0..infinity) |
EllipticPi[\[Alpha]^(2), (k)^2] == Divide[Pi,2]*Sum[Divide[Pochhammer[Divide[1,2], n],(n)!]*Sum[Divide[Pochhammer[Divide[1,2], m],(m)!]*(k)^(2*m)* \[Alpha]^(2*n - 2*m), {m, 0, n}, GenerateConditions->None], {n, 0, Infinity}, GenerateConditions->None] |
Aborted | Failure | Error | Skipped - Because timed out |
| 19.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\pi}{2}\sum_{n=0}^{\infty}\frac{\Pochhammersym{\tfrac{1}{2}}{n}}{n!}\sum_{m=0}^{n}\frac{\Pochhammersym{\tfrac{1}{2}}{m}}{m!}k^{2m}\alpha^{2n-2m} = \frac{\pi}{2}\AppellF{1}@{\tfrac{1}{2}}{\tfrac{1}{2}}{1}{1}{k^{2}}{\alpha^{2}}} | Error |
Divide[Pi,2]*Sum[Divide[Pochhammer[Divide[1,2], n],(n)!]*Sum[Divide[Pochhammer[Divide[1,2], m],(m)!]*(k)^(2*m)* \[Alpha]^(2*n - 2*m), {m, 0, n}, GenerateConditions->None], {n, 0, Infinity}, GenerateConditions->None] == Divide[Pi,2]*AppellF[1, , Divide[1,2], Divide[1,2], 1, 1]*(k)^(2)*\[Alpha]^(2) |
Missing Macro Error | Failure | Skip - symbolical successful subtest | Skipped - Because timed out |
| 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]] |
Successful | Successful | - | Successful [Tested: 1] |
| 19.5.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lambda = (1-\sqrt{k^{\prime}})/(2(1+\sqrt{k^{\prime}}))} | lambda = (1 -sqrt(sqrt(1 - (k)^(2))))/(2*(1 +sqrt(sqrt(1 - (k)^(2))))) |
\[Lambda] == (1 -Sqrt[Sqrt[1 - (k)^(2)]])/(2*(1 +Sqrt[Sqrt[1 - (k)^(2)]])) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 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}, GenerateConditions->None]))^(2) |
Failure | Failure | Error | Failed [1 / 3]
{DirectedInfinity[] <- {Rule[k, 1]} |
| 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}, GenerateConditions->None],1 + 2*Sum[(- 1)^(n)* (q)^((n)^(2)), {n, 1, Infinity}, GenerateConditions->None]] |
Failure | Failure | Error | Skipped - Because timed out |
| 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}, GenerateConditions->None] |
Failure | Failure | Error | Failed [30 / 30]
{Plus[DirectedInfinity[], Times[-1.5707963267948966, NProduct[Plus[1, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {m, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[k, 1], Rule[Subscript[k, m], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Plus[Complex[0.8428751774062981, -1.0782578237498217], Times[-1.5707963267948966, NProduct[Plus[1, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {m, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[k, 2], Rule[Subscript[k, m], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.5.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k_{m+1} = \frac{1-\sqrt{1-k_{m}^{2}}}{1+\sqrt{1-k_{m}^{2}}}} | (1 -sqrt(1 - k(k[m])^(2)))/(1 +sqrt(1 - k(k[m])^(2))) |
Divide[1 -Sqrt[1 - k(Subscript[k, m])^(2)],1 +Sqrt[1 - k(Subscript[k, m])^(2)]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 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 | - | Successful [Tested: 1] |
| 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 | - | Successful [Tested: 1] |
| 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 | - | Successful [Tested: 1] |
| 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 | - | Successful [Tested: 1] |
| 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 | - | Failed [1 / 1]
{Indeterminate <- {} |
| 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 | - | Failed [1 / 1]
{Indeterminate <- {} |
| 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 | - | Successful [Tested: 1] |
| 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 | - | Successful [Tested: 1] |
| 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)) |
Successful | Successful | - | Successful [Tested: 0] |
| 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 | Skip - No test values generated |
| 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] |
Successful | Failure | Skip - symbolical successful subtest | 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] |
Failure | Failure | Error | 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 | Failed [9 / 9]
{Indeterminate <- {Rule[k, 1], Rule[α, 1.5]}Complex[-1.593078238683172, 2.4424906541753444*^-15] <- {Rule[k, 2], Rule[α, 1.5]} |
| 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 | Failed [3 / 3] 3/3]: [[-1.404962946*I <- {alpha = 3/2}1.813799364 <- {alpha = 1/2} |
Failed [3 / 3]
{Complex[0.0, -1.4049629462081452] <- {Rule[α, 1.5]}1.813799364234218 <- {Rule[α, 0.5]} |
| 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 | - | Successful [Tested: 3] |
| 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 | Failed [2 / 10] 2/10]: [[.858407346 <- {phi = -2}-.858407346 <- {phi = 2} |
Successful [Tested: 10] |
| 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 | - | Failed [1 / 1]
{Indeterminate <- {} |
| 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 | - | Successful [Tested: 3] |
| 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, GenerateConditions->None] == 1 |
Successful | Successful | - | Successful [Tested: 3] |
| 19.6.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{1} = (\sin@@{\phi})\CarlsonellintRC@{1}{\cos^{2}@@{\phi}}} | Error |
EllipticF[\[Phi], (1)^2] == (Sin[\[Phi]])* 1/Sqrt[(Cos[\[Phi]])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(1)/((Cos[\[Phi]])^(2))] |
Missing Macro Error | Failure | - | Failed [2 / 10]
{DirectedInfinity[] <- {Rule[ϕ, -2]}DirectedInfinity[] <- {Rule[ϕ, 2]} |
| 19.6.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\sin@@{\phi})\CarlsonellintRC@{1}{\cos^{2}@@{\phi}} = \aGudermannian@{\phi}} | Error |
(Sin[\[Phi]])* 1/Sqrt[(Cos[\[Phi]])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(1)/((Cos[\[Phi]])^(2))] == InverseGudermannian[\[Phi]] |
Missing Macro Error | Failure | - | Successful [Tested: 4] |
| 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 | - | Successful [Tested: 3] |
| 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 | Failed [2 / 10] 2/10]: [[.858407346 <- {phi = -2}-.858407346 <- {phi = 2} |
Successful [Tested: 10] |
| 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 | - | Successful [Tested: 1] |
| 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 | - | Failed [2 / 10]
{-0.1814051463486368 <- {Rule[ϕ, -2]}0.1814051463486368 <- {Rule[ϕ, 2]} |
| 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 | - | Successful [Tested: 3] |
| 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, GenerateConditions->None] == 1 |
Successful | Successful | - | Successful [Tested: 3] |
| 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 | - | Successful [Tested: 9] |
| 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 | Failed [2 / 10] 2/10]: [[.858407346 <- {phi = -2}-.858407346 <- {phi = 2} |
Successful [Tested: 10] |
| 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 | Failed [2 / 10] 2/10]: [[-4.370079726 <- {phi = -2}4.370079726 <- {phi = 2} |
Successful [Tested: 10] |
| 19.6#Ex24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{\alpha^{2}}{0} = \CarlsonellintRC@{c-1}{c-\alpha^{2}}} | Error |
EllipticPi[\[Alpha]^(2), \[Phi],(0)^2] == 1/Sqrt[c - \[Alpha]^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(c - 1)/(c - \[Alpha]^(2))] |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Complex[0.4032669574270382, 0.8997227991212673] <- {Rule[c, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.17167863497284278, 0.9673069947694621] <- {Rule[c, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.6#Ex25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{\alpha^{2}}{1} = \frac{1}{1-\alpha^{2}}\left(\CarlsonellintRC@{c}{c-1}-\alpha^{2}\CarlsonellintRC@{c}{c-\alpha^{2}}\right)} | Error |
EllipticPi[\[Alpha]^(2), \[Phi],(1)^2] == Divide[1,1 - \[Alpha]^(2)]*(1/Sqrt[c - 1]*Hypergeometric2F1[1/2,1/2,3/2,1-(c)/(c - 1)]- \[Alpha]^(2)* 1/Sqrt[c - \[Alpha]^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(c)/(c - \[Alpha]^(2))]) |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Complex[0.39392267303966433, 0.8870442763896845] <- {Rule[c, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.15564928813724596, 0.9274825692848638] <- {Rule[c, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.6#Ex26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{1}{1} = \tfrac{1}{2}(\CarlsonellintRC@{c}{c-1}+\sqrt{c}(c-1)^{-1})} | Error |
EllipticPi[1, \[Phi],(1)^2] == Divide[1,2]*(1/Sqrt[c - 1]*Hypergeometric2F1[1/2,1/2,3/2,1-(c)/(c - 1)]+Sqrt[c]*(c - 1)^(- 1)) |
Missing Macro Error | Failure | - | Failed [60 / 60]
{Complex[0.42461599644771203, 0.9033982135739806] <- {Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.19222674503116347, 1.0138365568937844] <- {Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 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 | - | Successful [Tested: 30] |
| 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 | Failed [300 / 300] 300/300]: [[Float(infinity)+Float(infinity)*I <- {Delta = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, k = 1}-.4574406724+1.116997071*I <- {Delta = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Indeterminate <- {Rule[k, 1], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.8161437733664769, 0.6845645198965172] <- {Rule[k, 2], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[Float(infinity)+Float(infinity)*I <- {Delta = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, k = 1}-.5381374542+.4861981155*I <- {Delta = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Indeterminate <- {Rule[k, 1], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.12805668293605252, 0.0652384492706456] <- {Rule[k, 2], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | - | Successful [Tested: 9] |
| 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, GenerateConditions->None] == 1 |
Successful | Successful | - | Successful [Tested: 9] |
| 19.6#Ex32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x}{x} = x^{-1/2}} | Error |
1/Sqrt[x]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(x)] == (x)^(- 1/ 2) |
Missing Macro Error | Successful | - | Successful [Tested: 3] |
| 19.6#Ex33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{\lambda x}{\lambda y} = \lambda^{-1/2}\CarlsonellintRC@{x}{y}} | Error |
1/Sqrt[\[Lambda]*y]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Lambda]*x)/(\[Lambda]*y)] == \[Lambda]^(- 1/ 2)* 1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)] |
Missing Macro Error | Failure | - | Failed [75 / 180]
{Complex[2.0541315094196904, 2.1051836996148214] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[2.941079989400646, 0.036099349881403064] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.6#Ex35 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{0}{y} = \tfrac{1}{2}\pi y^{-1/2}} | Error |
1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(0)/(y)] == Divide[1,2]*Pi*(y)^(- 1/ 2) |
Missing Macro Error | Successful | - | Successful [Tested: 3] |
| 19.6#Ex36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{0}{y} = 0} | Error |
1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(0)/(y)] == 0 |
Missing Macro Error | Failure | - | Failed [3 / 3]
{Complex[0.0, -1.2825498301618643] <- {Rule[y, -1.5]}Complex[0.0, -2.221441469079183] <- {Rule[y, -0.5]} |
| 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 | Failed [1 / 3]
{Indeterminate <- {Rule[k, 1]} |
| 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 | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]}Complex[-2.220446049250313*^-16, -2.9198052634126777] <- {Rule[k, 2]} |
| 19.7#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{-ik^{\prime}/k} = k\compellintKk@{k^{\prime}}} | EllipticK(- I*sqrt(1 - (k)^(2))/ k) = k*EllipticK(sqrt(1 - (k)^(2))) |
EllipticK[(- I*Sqrt[1 - (k)^(2)]/ k)^2] == k*EllipticK[(Sqrt[1 - (k)^(2)])^2] |
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 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 | Failed [3 / 3] 3/3]: [[Float(infinity)+Float(infinity)*I <- {k = 1}.6e-9+.4691535424*I <- {k = 2} |
Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]}Complex[-5.551115123125783*^-16, 0.46915354293820644] <- {Rule[k, 2]} |
| 19.7#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{-ik^{\prime}/k} = (1/k)\compellintEk@{k^{\prime}}} | EllipticE(- I*sqrt(1 - (k)^(2))/ k) = (1/ k)* EllipticE(sqrt(1 - (k)^(2))) |
EllipticE[(- I*Sqrt[1 - (k)^(2)]/ k)^2] == (1/ k)* EllipticE[(Sqrt[1 - (k)^(2)])^2] |
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 19.7#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{1/k} = k(\compellintKk@{k}-\iunit\compellintKk@{k^{\prime}})} | EllipticK(1/ k) = k*(EllipticK(k)- I*EllipticK(sqrt(1 - (k)^(2)))) |
EllipticK[(1/ k)^2] == k*(EllipticK[(k)^2]- I*EllipticK[(Sqrt[1 - (k)^(2)])^2]) |
Failure | Failure | Error | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]}Complex[-2.220446049250313*^-16, 4.313031294999287] <- {Rule[k, 2]} |
| 19.7#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{1/k} = k(\compellintKk@{k}+\iunit\compellintKk@{k^{\prime}})} | EllipticK(1/ k) = k*(EllipticK(k)+ I*EllipticK(sqrt(1 - (k)^(2)))) |
EllipticK[(1/ k)^2] == k*(EllipticK[(k)^2]+ I*EllipticK[(Sqrt[1 - (k)^(2)])^2]) |
Failure | Failure | Error | Failed [1 / 3]
{Indeterminate <- {Rule[k, 1]} |
| 19.7#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{1/k^{\prime}} = k^{\prime}(\compellintKk@{k^{\prime}}+\iunit\compellintKk@{k})} | EllipticK(1/(sqrt(1 - (k)^(2)))) = sqrt(1 - (k)^(2))*(EllipticK(sqrt(1 - (k)^(2)))+ I*EllipticK(k)) |
EllipticK[(1/(Sqrt[1 - (k)^(2)]))^2] == Sqrt[1 - (k)^(2)]*(EllipticK[(Sqrt[1 - (k)^(2)])^2]+ I*EllipticK[(k)^2]) |
Failure | Failure | Error | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]}Complex[2.9198052634126785, -3.7351946687866775] <- {Rule[k, 2]} |
| 19.7#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{1/k^{\prime}} = k^{\prime}(\compellintKk@{k^{\prime}}-\iunit\compellintKk@{k})} | EllipticK(1/(sqrt(1 - (k)^(2)))) = sqrt(1 - (k)^(2))*(EllipticK(sqrt(1 - (k)^(2)))- I*EllipticK(k)) |
EllipticK[(1/(Sqrt[1 - (k)^(2)]))^2] == Sqrt[1 - (k)^(2)]*(EllipticK[(Sqrt[1 - (k)^(2)])^2]- I*EllipticK[(k)^2]) |
Failure | Failure | Error | Failed [1 / 3]
{Indeterminate <- {Rule[k, 1]} |
| 19.7#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{1/k} = (1/k)\left(\compellintEk@{k}+\iunit\compellintEk@{k^{\prime}}-{k^{\prime}}^{2}\compellintKk@{k}-\iunit k^{2}\compellintKk@{k^{\prime}}\right)} | EllipticE(1/ k) = (1/ k)*(EllipticE(k)+ I*EllipticE(sqrt(1 - (k)^(2)))-1 - (k)^(2)*EllipticK(k)- I*(k)^(2)* EllipticK(sqrt(1 - (k)^(2)))) |
EllipticE[(1/ k)^2] == (1/ k)*(EllipticE[(k)^2]+ I*EllipticE[(Sqrt[1 - (k)^(2)])^2]-1 - (k)^(2)*EllipticK[(k)^2]- I*(k)^(2)* EllipticK[(Sqrt[1 - (k)^(2)])^2]) |
Failure | Failure | Error | Failed [3 / 3]
{DirectedInfinity[] <- {Rule[k, 1]}Complex[3.4500631209220436, -1.8829831432620088] <- {Rule[k, 2]} |
| 19.7#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{1/k} = (1/k)\left(\compellintEk@{k}-\iunit\compellintEk@{k^{\prime}}-{k^{\prime}}^{2}\compellintKk@{k}+\iunit k^{2}\compellintKk@{k^{\prime}}\right)} | EllipticE(1/ k) = (1/ k)*(EllipticE(k)- I*EllipticE(sqrt(1 - (k)^(2)))-1 - (k)^(2)*EllipticK(k)+ I*(k)^(2)* EllipticK(sqrt(1 - (k)^(2)))) |
EllipticE[(1/ k)^2] == (1/ k)*(EllipticE[(k)^2]- I*EllipticE[(Sqrt[1 - (k)^(2)])^2]-1 - (k)^(2)*EllipticK[(k)^2]+ I*(k)^(2)* EllipticK[(Sqrt[1 - (k)^(2)])^2]) |
Failure | Failure | Error | Failed [3 / 3]
{DirectedInfinity[] <- {Rule[k, 1]}Complex[3.4500631209220436, -3.773902383124376] <- {Rule[k, 2]} |
| 19.7#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{1/k^{\prime}} = (1/k^{\prime})\left(\compellintEk@{k^{\prime}}-\iunit\compellintEk@{k}-k^{2}\compellintKk@{k^{\prime}}+\iunit{k^{\prime}}^{2}\compellintKk@{k}\right)} | EllipticE(1/(sqrt(1 - (k)^(2)))) = (1/(sqrt(1 - (k)^(2))))*(EllipticE(sqrt(1 - (k)^(2)))- I*EllipticE(k)- (k)^(2)* EllipticK(sqrt(1 - (k)^(2)))+ I*1 - (k)^(2)*EllipticK(k)) |
EllipticE[(1/(Sqrt[1 - (k)^(2)]))^2] == (1/(Sqrt[1 - (k)^(2)]))*(EllipticE[(Sqrt[1 - (k)^(2)])^2]- I*EllipticE[(k)^2]- (k)^(2)* EllipticK[(Sqrt[1 - (k)^(2)])^2]+ I*1 - (k)^(2)*EllipticK[(k)^2]) |
Failure | Failure | Error | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]}Complex[-1.1384238737361991, -2.262384972182541] <- {Rule[k, 2]} |
| 19.7#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{1/k^{\prime}} = (1/k^{\prime})\left(\compellintEk@{k^{\prime}}+\iunit\compellintEk@{k}-k^{2}\compellintKk@{k^{\prime}}-\iunit{k^{\prime}}^{2}\compellintKk@{k}\right)} | EllipticE(1/(sqrt(1 - (k)^(2)))) = (1/(sqrt(1 - (k)^(2))))*(EllipticE(sqrt(1 - (k)^(2)))+ I*EllipticE(k)- (k)^(2)* EllipticK(sqrt(1 - (k)^(2)))- I*1 - (k)^(2)*EllipticK(k)) |
EllipticE[(1/(Sqrt[1 - (k)^(2)]))^2] == (1/(Sqrt[1 - (k)^(2)]))*(EllipticE[(Sqrt[1 - (k)^(2)])^2]+ I*EllipticE[(k)^2]- (k)^(2)* EllipticK[(Sqrt[1 - (k)^(2)])^2]- I*1 - (k)^(2)*EllipticK[(k)^2]) |
Failure | Failure | Error | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]}Complex[-0.45287687829515355, -3.814134176668458] <- {Rule[k, 2]} |
| 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 | Failed [300 / 300] 300/300]: [[.1428695990-.263545696e-1*I <- {phi = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, k = 1}.749290340e-1-.334629029e-1*I <- {phi = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[0.020142137049999537, -0.0010462389457662757] <- {Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.015860617706546204, -0.003938067237051424] <- {Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[-.9970133474-.1125517221*I <- {phi = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, k = 1}-2.257467281-.7782721018*I <- {phi = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[-0.3893501368763376, 0.20738614458301174] <- {Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.6710974690872284, 0.0060773305020283] <- {Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [292 / 300] 292/300]: [[.926834363e-2-.484444094e-1*I <- {alpha = 3/2, phi = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, k = 1}-.130749569e-2-.277524276e-1*I <- {alpha = 3/2, phi = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [298 / 300]
{Complex[0.013291772923717082, -0.006719909387202905] <- {Rule[k, 1], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.00953602334602252, -0.007394575555177196] <- {Rule[k, 2], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.8#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n+1} = \frac{a_{n}+g_{n}}{2}} | a[n + 1] = (a[n]+ g[n])/(2) |
Subscript[a, n + 1] == Divide[Subscript[a, n]+ Subscript[g, n],2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.8#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{n+1} = \sqrt{a_{n}g_{n}}} | g[n + 1] = sqrt(a[n]*g[n]) |
Subscript[g, n + 1] == Sqrt[Subscript[a, n]*Subscript[g, n]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.8.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{n} = \sqrt{a_{n}^{2}-g_{n}^{2}}} | sqrt(a(a[n])^(2)- g(g[n])^(2)) |
Sqrt[a(Subscript[a, n])^(2)- g(Subscript[g, n])^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.8.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{n+1} = \frac{a_{n}-g_{n}}{2}} | c[n + 1] = (a[n]- g[n])/(2) |
Subscript[c, n + 1] == Divide[Subscript[a, n]- Subscript[g, n],2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 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 | Missing Macro Error | Error | Skip - symbolical successful subtest |
| 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}, GenerateConditions->None] Integrate[Divide[1,Sqrt[t*(t + a(Subscript[a, 0])^(2))*(t + g(Subscript[g, 0])^(2))]], {t, 0, Infinity}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 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 | Missing Macro Error | Error | - |
| 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 | Missing Macro Error | Error | - |
| 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 | Missing Macro Error | Error | - |
| 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 | Missing Macro Error | Error | - |
| 19.8#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{n+1} = \frac{p_{n}^{2}+a_{n}g_{n}}{2p_{n}}} | p[n + 1] (p(p[n])^(2)+ a[n]*g[n])/(2*p[n]) |
Subscript[p, n + 1] Divide[p(Subscript[p, n])^(2)+ Subscript[a, n]*Subscript[g, n],2*Subscript[p, n]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.8#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \varepsilon_{n} = \frac{p_{n}^{2}-a_{n}g_{n}}{p_{n}^{2}+a_{n}g_{n}}} | (p(p[n])^(2)- a[n]*g[n])/(p(p[n])^(2)+ a[n]*g[n]) |
Divide[p(Subscript[p, n])^(2)- Subscript[a, n]*Subscript[g, n],p(Subscript[p, n])^(2)+ Subscript[a, n]*Subscript[g, n]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.8#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{n+1} = \tfrac{1}{2}Q_{n}\varepsilon_{n}} | Q[n + 1] = (1)/(2)*Q[n]*varepsilon[n] |
Subscript[Q, n + 1] == Divide[1,2]*Subscript[Q, n]*Subscript[\[CurlyEpsilon], n] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.8.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 | Missing Macro Error | Error | - |
| 19.8.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{0}^{2} = 1-(k^{2}/\alpha^{2})} | (p[0])^(2) = 1 -((k)^(2)/ (alpha)^(2)) |
(Subscript[p, 0])^(2) == 1 -((k)^(2)/ \[Alpha]^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 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 | Failed [30 / 30]
{DirectedInfinity[] <- {Rule[k, 1], Rule[Subscript[k, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.44075376931664, -1.6191557371087932] <- {Rule[k, 2], Rule[Subscript[k, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [30 / 30]
{Indeterminate <- {Rule[k, 1], Rule[Subscript[k, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.595329372049606, 0.2521613076710463] <- {Rule[k, 2], Rule[Subscript[k, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[.2591790565-.226164263e-1*I <- {phi = 1/2*3^(1/2)+1/2*I, k[1] = 1/2*3^(1/2)+1/2*I, k = 1}.8581261265-.11942686e-2*I <- {phi = 1/2*3^(1/2)+1/2*I, k[1] = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[0.15619877563526813, 0.03685530383845256] <- {Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[k, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.6672885103059906, -0.24203301849204312] <- {Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[k, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[-.627821156e-1-.413169945e-1*I <- {phi = 1/2*3^(1/2)+1/2*I, k[1] = 1/2*3^(1/2)+1/2*I, k = 1}.886069620e-1-.4575597e-3*I <- {phi = 1/2*3^(1/2)+1/2*I, k[1] = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[-0.0022565574667213206, -0.009009769525654576] <- {Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[k, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.11756483394447081, -0.05872123913100852] <- {Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[k, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.8.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2(k^{2}-\alpha^{2})\incellintPik@{\phi}{\alpha^{2}}{k} = \frac{\omega^{2}-\alpha^{2}}{1+k^{\prime}}\incellintPik@{\phi_{1}}{\alpha_{1}^{2}}{k_{1}}+k^{2}\incellintFk@{\phi}{k}-{(1+k^{\prime})\alpha_{1}^{2}\CarlsonellintRC@{c_{1}}{c_{1}-\alpha_{1}^{2}}}} | Error |
2*((k)^(2)- \[Alpha]^(2))* EllipticPi[\[Alpha]^(2), \[Phi],(k)^2] == EllipticPi[\[Alpha](Subscript[\[Alpha], 1])^(2), Subscript[\[Phi], 1],(Subscript[k, 1])^2]+ (k)^(2)* EllipticF[\[Phi], (k)^2]-(1 +Sqrt[1 - (k)^(2)])* 1/Sqrt[Subscript[c, 1]- \[Alpha](Subscript[\[Alpha], 1])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(Subscript[c, 1])/(Subscript[c, 1]- \[Alpha](Subscript[\[Alpha], 1])^(2))] |
Missing Macro Error | Aborted | - | Failed [300 / 300]
{Complex[-1.4115811709537147, -1.2227387134851169] <- {Rule[k, 1], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ω, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[k, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[α, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.5976966939439394, -1.230515427208163] <- {Rule[k, 2], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ω, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[k, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[α, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[.716161018e-1+.1278882161*I <- {phi = 1/2*3^(1/2)+1/2*I, k[2] = 1/2*3^(1/2)+1/2*I, phi[2] = 1/2*3^(1/2)+1/2*I, k = 1}-.163142760e-1+.3519262665*I <- {phi = 1/2*3^(1/2)+1/2*I, k[2] = 1/2*3^(1/2)+1/2*I, phi[2] = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[0.0030858847214221274, 0.01883659064247678] <- {Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[k, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[ϕ, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.11075679050380455, 0.16335572999260056] <- {Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[k, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[ϕ, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[-.251128463-.1652679776*I <- {phi = 1/2*3^(1/2)+1/2*I, k[2] = 1/2*3^(1/2)+1/2*I, phi[2] = 1/2*3^(1/2)+1/2*I, k = 1}.549972877-.903450862e-1*I <- {phi = 1/2*3^(1/2)+1/2*I, k[2] = 1/2*3^(1/2)+1/2*I, phi[2] = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[-0.009026229866885283, -0.03603907810261833] <- {Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[k, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[ϕ, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.42447097038130677, 0.1345883883024661] <- {Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[k, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[ϕ, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [299 / 300] 299/300]: [[-.3025119160-.7226109033*I <- {phi = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, k[1] = 1/2*3^(1/2)+1/2*I, psi[1] = 1/2*3^(1/2)+1/2*I, k = 1}-.6401936029-.6817361311*I <- {phi = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, k[1] = 1/2*3^(1/2)+1/2*I, psi[1] = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [299 / 300]
{Complex[-0.11940620612760577, -0.19771875715838422] <- {Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[k, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[ψ, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.15464125790413003, -0.13739720920586462] <- {Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[k, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[ψ, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[-.5555013192-.1267358774*I <- {phi = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, k[1] = 1/2*3^(1/2)+1/2*I, psi[1] = 1/2*3^(1/2)+1/2*I, k = 1}-1.589246368-2.046785663*I <- {phi = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, k[1] = 1/2*3^(1/2)+1/2*I, psi[1] = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[-0.22091089534718378, -0.1170454776590783] <- {Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[k, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[ψ, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.9299237807056446, -0.7272990802320405] <- {Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[k, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[ψ, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.8.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho\incellintPik@{\phi}{\alpha^{2}}{k} = \frac{4}{1+k^{\prime}}\incellintPik@{\psi_{1}}{\alpha_{1}^{2}}{k_{1}}+(\rho-1)\incellintFk@{\phi}{k}-\CarlsonellintRC@{c-1}{c-\alpha^{2}}} | Error |
\[Rho]*EllipticPi[\[Alpha]^(2), \[Phi],(k)^2] == EllipticPi[\[Alpha](Subscript[\[Alpha], 1])^(2), Subscript[\[Psi], 1],(Subscript[k, 1])^2]+(\[Rho]- 1)* EllipticF[\[Phi], (k)^2]- 1/Sqrt[c - \[Alpha]^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(c - 1)/(c - \[Alpha]^(2))] |
Missing Macro Error | Failure | - | Skipped - Because timed out |
| 19.9#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{4} \leq \compellintKk@{k}+\ln@@{k^{\prime}}} | ln(4) <= EllipticK(k)+ ln(sqrt(1 - (k)^(2))) |
Log[4] <= EllipticK[(k)^2]+ Log[Sqrt[1 - (k)^(2)]] |
Failure | Failure | Error | Failed [3 / 3]
{LessEqual[1.3862943611198906, Indeterminate] <- {Rule[k, 1]}LessEqual[1.3862943611198906, Complex[1.392181321740353, 0.49253850304507485]] <- {Rule[k, 2]} |
| 19.9#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k}+\ln@@{k^{\prime}} \leq \pi/2} | EllipticK(k)+ ln(sqrt(1 - (k)^(2))) <= Pi/ 2 |
EllipticK[(k)^2]+ Log[Sqrt[1 - (k)^(2)]] <= Pi/ 2 |
Failure | Failure | Error | Failed [3 / 3]
{LessEqual[Indeterminate, 1.5707963267948966] <- {Rule[k, 1]}LessEqual[Complex[1.392181321740353, 0.49253850304507485], 1.5707963267948966] <- {Rule[k, 2]} |
| 19.9#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 \leq \compellintEk@{k}} | 1 <= EllipticE(k) |
1 <= EllipticE[(k)^2] |
Failure | Failure | Successful [Tested: 3] | Failed [2 / 3]
{LessEqual[1.0, Complex[0.40629888645996043, 1.343854231387098]] <- {Rule[k, 2]}LessEqual[1.0, Complex[0.2655964076372759, 2.498348127732516]] <- {Rule[k, 3]} |
| 19.9#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{k} \leq \pi/2} | EllipticE(k) <= Pi/ 2 |
EllipticE[(k)^2] <= Pi/ 2 |
Failure | Failure | Successful [Tested: 3] | Failed [2 / 3]
{LessEqual[Complex[0.40629888645996043, 1.343854231387098], 1.5707963267948966] <- {Rule[k, 2]}LessEqual[Complex[0.2655964076372759, 2.498348127732516], 1.5707963267948966] <- {Rule[k, 3]} |
| 19.9#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 \leq (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 | Failed [3 / 3]
{LessEqual[1.0, DirectedInfinity[], DirectedInfinity[]] <- {Rule[k, 1], Rule[α, 0.5]}LessEqual[1.0, Complex[0.4804983499812288, -0.6957733039705274], Complex[0.0, -0.5773502691896258]] <- {Rule[k, 2], Rule[α, 0.5]} |
| 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 | Failed [3 / 3]
{Less[1.0, Indeterminate] <- {Rule[k, 1]}Less[0.625, Complex[0.7573351019929213, 0.13305010797062605]] <- {Rule[k, 2]} |
| 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 | Failed [3 / 3]
{Less[Indeterminate, 1.0] <- {Rule[k, 1]}Less[Complex[0.7573351019929213, 0.13305010797062605], 0.25] <- {Rule[k, 2]} |
| 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 | Failed [3 / 3]
{Less[9.0, Indeterminate] <- {Rule[k, 1]}Less[9.0, Complex[9.088021223915057, 1.5966012956475137]] <- {Rule[k, 2]} |
| 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 | Failed [3 / 3]
{Less[Indeterminate, 9.096] <- {Rule[k, 1]}Less[Complex[9.088021223915057, 1.5966012956475137], 9.096] <- {Rule[k, 2]} |
| 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} \leq \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 [Tested: 3] | Failed [2 / 3]
{LessEqual[Complex[0.2518251425072316, 0.8700591952646104], Complex[0.2586579046113418, 0.8555241748808654]] <- {Rule[k, 2]}LessEqual[Complex[0.1858923839966674, 1.6059081831429025], Complex[0.16908392457168991, 1.5904978163720476]] <- {Rule[k, 3]} |
| 19.9.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\compellintEk@{k} \leq \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 [Tested: 3] | Failed [2 / 3]
{LessEqual[Complex[0.2586579046113418, 0.8555241748808654], Complex[0.0, 1.0]] <- {Rule[k, 2]}LessEqual[Complex[0.16908392457168991, 1.5904978163720476], Complex[0.0, 1.8708286933869707]] <- {Rule[k, 3]} |
| 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 | Failed [3 / 3]
{False <- {Rule[k, 1]}Less[Complex[0.8314429455293103, 0.8983332083070389], Complex[0.762166367418117, 0.9750101446769989]] <- {Rule[k, 2]} |
| 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 | Failed [2 / 3]
{Less[Complex[0.762166367418117, 0.9750101446769989], Complex[0.6931471805599452, 1.0471975511965976]] <- {Rule[k, 2]}Less[Complex[0.7130154358988758, 1.1147297033963086], Complex[0.6931471805599453, 1.2309594173407747]] <- {Rule[k, 3]} |
| 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 | Failed [3 / 3]
{Less[2.0, DirectedInfinity[]] <- {Rule[k, 1]}Less[Complex[0.0, -0.7071067811865475], Complex[0.13896654948167025, -0.7709822125950203]] <- {Rule[k, 2]} |
| 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 | Failed [3 / 3]
{Less[DirectedInfinity[], DirectedInfinity[]] <- {Rule[k, 1]}Less[Complex[0.13896654948167025, -0.7709822125950203], Complex[0.2534656958546175, -0.6119203205285516]] <- {Rule[k, 2]} |
| 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 | Failed [3 / 3]
{Less[1.1547005383792517, DirectedInfinity[]] <- {Rule[k, 1]}Less[DirectedInfinity[], Complex[-1.2621629410274844, 1.800642588058783]] <- {Rule[k, 2]} |
| 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 | Failed [3 / 3]
{False <- {Rule[k, 1]}Less[Complex[0.0, 1.7320508075688772], Complex[-0.5907718728609501, 0.8386174564999851]] <- {Rule[k, 2]} |
| 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 | Failed [2 / 3]
{Less[Complex[-0.5907718728609501, 0.8386174564999851], Complex[-0.4999999999999999, 0.8660254037844386]] <- {Rule[k, 2]}Less[Complex[-1.9604512687154212, 1.5690726247192568], Complex[-1.7500000000000004, 1.4142135623730951]] <- {Rule[k, 3]} |
| 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] |
Error | Failure | - | Error |
| 19.9.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi \leq \incellintFk@{\phi}{k}} | phi <= EllipticF(sin(phi), k) |
\[Phi] <= EllipticF[\[Phi], (k)^2] |
Failure | Failure | Failed [4 / 30] 4/30]: [[-1.500000000 <= -3.340677542 <- {phi = -3/2, k = 1}-.5000000000 <= -.5222381033 <- {phi = -1/2, k = 1} |
Failed [28 / 30]
{LessEqual[Complex[0.43301270189221935, 0.24999999999999997], Complex[0.43180375739814203, 0.27142936483528934]] <- {Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}LessEqual[Complex[0.43301270189221935, 0.24999999999999997], Complex[0.3965687056216178, 0.33175091278780894]] <- {Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.9.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} \leq \phi} | EllipticE(sin(phi), k) <= phi |
EllipticE[\[Phi], (k)^2] <= \[Phi] |
Failure | Failure | Failed [4 / 30] 4/30]: [[-.9974949866 <= -1.500000000 <- {phi = -3/2, k = 1}-.4794255386 <= -.5000000000 <- {phi = -1/2, k = 1} |
Failed [27 / 30]
{LessEqual[Complex[0.43278851685803155, 0.22929764467344024], Complex[0.43301270189221935, 0.24999999999999997]] <- {Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}LessEqual[Complex[0.44208095936294645, 0.16535187593702125], Complex[0.43301270189221935, 0.24999999999999997]] <- {Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.9.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{\alpha^{2}}{0} \leq \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 | Failed [8 / 90] 8/90]: [[-.6351972518 <= -.6692391842 <- {alpha = 3/2, phi = -1/2, k = 1}-.6351972518 <= -.9273807742 <- {alpha = 3/2, phi = -1/2, k = 2} |
Failed [84 / 90]
{LessEqual[Complex[0.4032669574270382, 0.3492210121777662], Complex[0.39392267303966433, 0.37152709024037445]] <- {Rule[k, 1], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}LessEqual[Complex[0.4032669574270382, 0.3492210121777662], Complex[0.33490711362096304, 0.4200642464932446]] <- {Rule[k, 2], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [16 / 300] 16/300]: [[7.945282179 < 1.089299717 <- {Delta = -3/2, phi = -1/2, k = 1}7.945282179 < 1.412977582 <- {Delta = -3/2, phi = -1/2, k = 2} |
Failed [284 / 300]
{Less[Complex[1.261572446843062, -0.07667841479591199], Complex[1.0384958486950706, 0.07695378095553612]] <- {Rule[k, 1], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Less[Complex[1.261572446843062, -0.07667841479591199], Complex[1.0325857379409573, 0.21946385233164167]] <- {Rule[k, 2], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [20 / 300] 20/300]: [[1.675417084 < 1.170093898 <- {Delta = -3/2, phi = -2, k = 1}1.675417084 < 1.170093898 <- {Delta = -3/2, phi = 2, k = 1} |
Failed [298 / 300]
{Less[Complex[1.0384958486950706, 0.07695378095553612], Complex[1.2731409874856745, -0.17545913345292982]] <- {Rule[k, 1], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Less[Complex[1.0325857379409573, 0.21946385233164167], Complex[1.2731409874856745, -0.17545913345292982]] <- {Rule[k, 2], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [6 / 300] 6/300]: [[1. < .4615167558 <- {Delta = -1/2, phi = -1/2, k = 1}1. < .5986532627 <- {Delta = -1/2, phi = -1/2, k = 2} |
Failed [288 / 300]
{Less[1.0, Complex[0.9573719244599448, 0.16621131448588694]] <- {Rule[k, 1], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Less[1.0, Complex[0.9388814261604885, 0.2980132161872323]] <- {Rule[k, 2], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [20 / 300] 20/300]: [[3.582850518 < 1.002508151 <- {Delta = 3/2, phi = -3/2, k = 1}3.582850518 < 1.002508151 <- {Delta = 3/2, phi = 3/2, k = 1} |
Failed [296 / 300]
{Less[Complex[0.9573719244599448, 0.16621131448588694], Complex[1.7102149955099495, -0.29913282294542826]] <- {Rule[k, 1], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Less[Complex[0.9388814261604885, 0.2980132161872323], Complex[1.3149325512421652, -0.4880625346303866]] <- {Rule[k, 2], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.9.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{k} = \frac{2}{\pi}\compellintKk@{k^{\prime}}\ln@{\frac{4}{\Delta+\cos@@{\phi}}}-\theta\Delta^{2}} | EllipticF(sin(phi), k) = (2)/(Pi)*EllipticK(sqrt(1 - (k)^(2)))*ln((4)/(Delta + cos(phi)))- theta*(Delta)^(2) |
EllipticF[\[Phi], (k)^2] == Divide[2,Pi]*EllipticK[(Sqrt[1 - (k)^(2)])^2]*Log[Divide[4,\[CapitalDelta]+ Cos[\[Phi]]]]- \[Theta]*\[CapitalDelta]^(2) |
Failure | Failure | Failed [30 / 30] 30/30]: [[2.264395299+.9232968251*I <- {Delta = 1/2*3^(1/2)+1/2*I, phi = 3/2, theta = 1/2, k = 1}-.185868314e-1+.7122804653*I <- {Delta = 1/2*3^(1/2)+1/2*I, phi = 1/2, theta = 1/2, k = 1} |
Failed [30 / 30]
{Complex[1.4412941413043292, 0.5689187621917111] <- {Rule[k, 1], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, 0.5], Rule[ϕ, 1.5]}Complex[-0.5132046492108906, 0.2967418012807382] <- {Rule[k, 1], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, 0.5], Rule[ϕ, 0.5]} |
| 19.9.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L \leq \incellintFk@{\phi}{k}} | L <= EllipticF(sin(phi), k) |
L <= EllipticF[\[Phi], (k)^2] |
Failure | Failure | Failed [24 / 300] 24/300]: [[-1.500000000 <= -3.340677542 <- {L = -3/2, phi = -3/2, k = 1}-1.500000000 <= -1.523452443 <- {L = -3/2, phi = -2, k = 1} |
Failed [288 / 300]
{LessEqual[Complex[0.43301270189221935, 0.24999999999999997], Complex[0.43180375739814203, 0.27142936483528934]] <- {Rule[k, 1], Rule[L, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}LessEqual[Complex[0.43301270189221935, 0.24999999999999997], Complex[0.3965687056216178, 0.33175091278780894]] <- {Rule[k, 2], Rule[L, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.9.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{k} \leq \sqrt{UL}} | EllipticF(sin(phi), k) <= sqrt(U*L) |
EllipticF[\[Phi], (k)^2] <= Sqrt[U*L] |
Failure | Failure | Successful [Tested: 300] | Failed [300 / 300]
{LessEqual[Complex[0.43180375739814203, 0.27142936483528934], Complex[0.43301270189221935, 0.24999999999999997]] <- {Rule[k, 1], Rule[L, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[U, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}LessEqual[Complex[0.3965687056216178, 0.33175091278780894], Complex[0.43301270189221935, 0.24999999999999997]] <- {Rule[k, 2], Rule[L, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[U, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.9.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{UL} \leq \tfrac{1}{2}(U+L)} | sqrt(U*L) <= (1)/(2)*(U + L) |
Sqrt[U*L] <= Divide[1,2]*(U + L) |
Failure | Failure | Failed [9 / 100] 9/100]: [[1.500000000 <= -1.500000000 <- {L = -3/2, U = -3/2}.8660254040 <= -1. <- {L = -3/2, U = -1/2} |
Failed [91 / 100]
{LessEqual[Complex[0.43301270189221935, 0.24999999999999997], Complex[0.43301270189221935, 0.24999999999999997]] <- {Rule[L, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[U, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}LessEqual[Complex[0.12940952255126037, 0.48296291314453416], Complex[0.09150635094610973, 0.34150635094610965]] <- {Rule[L, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[U, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.9.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}(U+L) \leq U} | (1)/(2)*(U + L) <= U |
Divide[1,2]*(U + L) <= U |
Failure | Failure | Failed [15 / 100] 15/100]: [[-1.750000000 <= -2. <- {L = -3/2, U = -2}0. <= -1.500000000 <- {L = 3/2, U = -3/2} |
Failed [79 / 100]
{LessEqual[Complex[0.43301270189221935, 0.24999999999999997], Complex[0.43301270189221935, 0.24999999999999997]] <- {Rule[L, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[U, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}LessEqual[Complex[0.09150635094610973, 0.34150635094610965], Complex[-0.2499999999999999, 0.43301270189221935]] <- {Rule[L, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[U, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[.1841715885+.458206673e-1*I <- {L = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I}-.197696883e-1+.4084290873*I <- {L = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, sigma = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[0.008169183554908921, 0.015254361571334585] <- {Rule[L, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[σ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.6990489693230986, -0.19299436497537428] <- {Rule[L, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[σ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[.451553750e-1-.1773780507*I <- {U = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, k = 1}.3250459090-.1674857034*I <- {U = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[0.0012089444940770466, -0.021429364835289427] <- {Rule[k, 1], Rule[U, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.04320077983427789, -0.07655275524887523] <- {Rule[k, 2], Rule[U, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.10#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@{x/y} = (x-y)\CarlsonellintRC@{\tfrac{1}{4}(x+y)^{2}}{xy}} | Error |
Log[x/ y] == (x - y)* 1/Sqrt[x*y]*Hypergeometric2F1[1/2,1/2,3/2,1-(Divide[1,4]*(x + y)^(2))/(x*y)] |
Missing Macro Error | Failure | - | Failed [12 / 18]
{Complex[0.0, 6.283185307179586] <- {Rule[x, 1.5], Rule[y, -1.5]}Indeterminate <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.10#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atan@{x/y} = x\CarlsonellintRC@{y^{2}}{y^{2}+x^{2}}} | Error |
ArcTan[x/ y] == x*1/Sqrt[(y)^(2)+ (x)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((y)^(2))/((y)^(2)+ (x)^(2))] |
Missing Macro Error | Failure | - | Failed [9 / 18]
{-1.5707963267948966 <- {Rule[x, 1.5], Rule[y, -1.5]}-2.498091544796509 <- {Rule[x, 1.5], Rule[y, -0.5]} |
| 19.10#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atanh@{x/y} = x\CarlsonellintRC@{y^{2}}{y^{2}-x^{2}}} | Error |
ArcTanh[x/ y] == x*1/Sqrt[(y)^(2)- (x)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((y)^(2))/((y)^(2)- (x)^(2))] |
Missing Macro Error | Failure | - | Failed [15 / 18]
{Indeterminate <- {Rule[x, 1.5], Rule[y, -1.5]}Indeterminate <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.10#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asin@{x/y} = x\CarlsonellintRC@{y^{2}-x^{2}}{y^{2}}} | Error |
ArcSin[x/ y] == x*1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((y)^(2)- (x)^(2))/((y)^(2))] |
Missing Macro Error | Failure | - | Failed [9 / 18]
{-3.141592653589793 <- {Rule[x, 1.5], Rule[y, -1.5]}Complex[-3.141592653589793, 3.525494348078172] <- {Rule[x, 1.5], Rule[y, -0.5]} |
| 19.10#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asinh@{x/y} = x\CarlsonellintRC@{y^{2}+x^{2}}{y^{2}}} | Error |
ArcSinh[x/ y] == x*1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((y)^(2)+ (x)^(2))/((y)^(2))] |
Missing Macro Error | Failure | - | Failed [9 / 18]
{Complex[-1.7627471740390859, 0.0] <- {Rule[x, 1.5], Rule[y, -1.5]}Complex[-3.6368929184641337, 0.0] <- {Rule[x, 1.5], Rule[y, -0.5]} |
| 19.10#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acos@{x/y} = (y^{2}-x^{2})^{1/2}\CarlsonellintRC@{x^{2}}{y^{2}}} | Error |
ArcCos[x/ y] == ((y)^(2)- (x)^(2))^(1/ 2)* 1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((y)^(2))] |
Missing Macro Error | Failure | - | Failed [12 / 18]
{Indeterminate <- {Rule[x, 1.5], Rule[y, -1.5]}Indeterminate <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.10#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acosh@{x/y} = (x^{2}-y^{2})^{1/2}\CarlsonellintRC@{x^{2}}{y^{2}}} | Error |
ArcCosh[x/ y] == ((x)^(2)- (y)^(2))^(1/ 2)* 1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((y)^(2))] |
Missing Macro Error | Failure | - | Failed [12 / 18]
{Indeterminate <- {Rule[x, 1.5], Rule[y, -1.5]}Indeterminate <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.10.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\sinh@@{\phi})\CarlsonellintRC@{1}{\cosh^{2}@@{\phi}} = \Gudermannian@{\phi}} | Error |
(Sinh[\[Phi]])* 1/Sqrt[(Cosh[\[Phi]])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(1)/((Cosh[\[Phi]])^(2))] == Gudermannian[\[Phi]] |
Missing Macro Error | Failure | - | Successful [Tested: 6] |
| 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 | Failed [300 / 300] 300/300]: [[.8208700290+.6773780507*I <- {phi = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 1}.4831883421+.7182528229*I <- {phi = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[0.43180375739814203, 0.27142936483528934] <- {Rule[k, 1], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.3965687056216178, 0.33175091278780894] <- {Rule[k, 2], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[.5188815884-.3712110352*I <- {phi = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 1}-.324003006-2.889566484*I <- {phi = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[0.41998937174924766, 0.11250711558240023] <- {Rule[k, 1], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.3908843789278109, -0.3018102404271388] <- {Rule[k, 2], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[-.360132946e-1+.3498736067*I <- {Delta = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 1}.3023079579-.441042741e-1*I <- {Delta = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[0.06008432780660544, 0.09466439987688165] <- {Rule[k, 1], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.1274461431695849, -0.029704144406044533] <- {Rule[k, 2], Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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]]] |
Translation Error | Translation Error | - | - |
| 19.11.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\theta}{\alpha^{2}}{k}+\incellintPik@{\phi}{\alpha^{2}}{k} = \incellintPik@{\psi}{\alpha^{2}}{k}-\alpha^{2}\CarlsonellintRC@{\gamma-\delta}{\gamma}} | Error |
EllipticPi[\[Alpha]^(2), \[Theta],(k)^2]+ EllipticPi[\[Alpha]^(2), \[Phi],(k)^2] == EllipticPi[\[Alpha]^(2), \[Psi],(k)^2]- \[Alpha]^(2)* 1/Sqrt[\[Gamma]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Gamma]- \[Delta])/(\[Gamma])] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Complex[2.431737700775111, 0.07689658395417326] <- {Rule[k, 1], Rule[α, 1.5], Rule[γ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.648685299290325, -1.4197583822626343] <- {Rule[k, 2], Rule[α, 1.5], Rule[γ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.11.E6_5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{\gamma-\delta}{\gamma} = \frac{-1}{\sqrt{\delta}}\atan@{\frac{\sqrt{\delta}\sin@@{\theta}\sin@@{\phi}\sin@@{\psi}}{\alpha^{2}-1-\alpha^{2}\cos@@{\theta}\cos@@{\phi}\cos@@{\psi}}}} | Error |
1/Sqrt[\[Gamma]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Gamma]- \[Delta])/(\[Gamma])] == Divide[- 1,Sqrt[\[Delta]]]*ArcTan[Divide[Sqrt[\[Delta]]*Sin[\[Theta]]*Sin[\[Phi]]*Sin[\[Psi]],\[Alpha]^(2)- 1 - \[Alpha]^(2)* Cos[\[Theta]]*Cos[\[Phi]]*Cos[\[Psi]]]] |
Missing Macro Error | Translation Error | - | - |
| 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 | Failed [300 / 300]
{DirectedInfinity[] <- {Rule[k, 1], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.04973776616306258, 1.7417596493254397] <- {Rule[k, 2], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [295 / 300] 295/300]: [[.940848258e-1+.952154806e-1*I <- {phi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 1}-.829018303-3.772436995*I <- {phi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [297 / 300]
{Complex[-0.2691514567553243, 0.26012051423236426] <- {Rule[k, 1], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.06105092961961717, -1.8070495799711206] <- {Rule[k, 2], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[Float(infinity)+Float(infinity)*I <- {phi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 1}1.112198033+1.184536461*I <- {phi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{DirectedInfinity[] <- {Rule[k, 1], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.0561283793604441, 1.210195136063891] <- {Rule[k, 2], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.11.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{\alpha^{2}}{k} = \compellintPik@{\alpha^{2}}{k}-\incellintPik@{\theta}{\alpha^{2}}{k}-\alpha^{2}\CarlsonellintRC@{\gamma-\delta}{\gamma}} | Error |
EllipticPi[\[Alpha]^(2), \[Phi],(k)^2] == EllipticPi[\[Alpha]^(2), (k)^2]- EllipticPi[\[Alpha]^(2), \[Theta],(k)^2]- \[Alpha]^(2)* 1/Sqrt[\[Gamma]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Gamma]- \[Delta])/(\[Gamma])] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{DirectedInfinity[] <- {Rule[k, 1], Rule[α, 1.5], Rule[γ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[2.2835000786563655, -0.476202278380103] <- {Rule[k, 2], Rule[α, 1.5], Rule[γ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[-.8208700290-.6773780507*I <- {psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 1}-.4831883421-.7182528229*I <- {psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[-0.43180375739814203, -0.27142936483528934] <- {Rule[k, 1], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.3965687056216178, -0.33175091278780894] <- {Rule[k, 2], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[-.5188815884+.3712110352*I <- {psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 1}.324003006+2.889566484*I <- {psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [298 / 300]
{Complex[-0.41998937174924766, -0.11250711558240023] <- {Rule[k, 1], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.3908843789278109, 0.3018102404271388] <- {Rule[k, 2], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[.6382547213-.68319321e-2*I <- {psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 1}1.291602175-.5372399851*I <- {psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[0.22600457397095797, 0.19313483829287414] <- {Rule[k, 1], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.33144266284556045, -0.05654646036238595] <- {Rule[k, 2], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[-.4299370879-.441018886e-1*I <- {psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 1}-1.378631246+.6589669897*I <- {psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[-0.21639778041374116, -0.09902593860776912] <- {Rule[k, 1], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.2801868441200064, 0.09163936360272593] <- {Rule[k, 2], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[.3459933254+.2199626413*I <- {Delta = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I}-1.183718368+.7410028953*I <- {Delta = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, theta = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[0.13267626462165183, 0.09545710280323466] <- {Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.6075958421397494, -0.12937331954381406] <- {Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[-.1386531520-.3275237699*I <- {Delta = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I}.3585693461+.5385011568*I <- {Delta = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, theta = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[-0.027928525698177165, -0.06433717895055871] <- {Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.11337825659380207, -0.16573354274294425] <- {Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[.1382279959+.6687205345*I <- {Delta = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I}-.8192630216+.6110829935*I <- {Delta = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, theta = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[0.12433851209893465, 0.1415108829927562] <- {Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.5756669065605976, -0.05657247148971478] <- {Rule[Δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.11.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\psi}{\alpha^{2}}{k} = 2\incellintPik@{\theta}{\alpha^{2}}{k}+\alpha^{2}\CarlsonellintRC@{\gamma-\delta}{\gamma}} | Error |
EllipticPi[\[Alpha]^(2), \[Psi],(k)^2] == 2*EllipticPi[\[Alpha]^(2), \[Theta],(k)^2]+ \[Alpha]^(2)* 1/Sqrt[\[Gamma]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Gamma]- \[Delta])/(\[Gamma])] |
Missing Macro Error | Aborted | - | Failed [300 / 300]
{Complex[-0.6318505653554005, -0.11296244472006367] <- {Rule[k, 1], Rule[α, 1.5], Rule[δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.5728350059366992, -0.1614996009729338] <- {Rule[k, 2], Rule[α, 1.5], Rule[δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ψ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 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}, GenerateConditions->None] |
Failure | Failure | Error | Skip - No test values generated |
| 19.12.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{k} = 1+\frac{1}{2}\sum_{m=0}^{\infty}\frac{\Pochhammersym{\tfrac{1}{2}}{m}\Pochhammersym{\tfrac{3}{2}}{m}}{\Pochhammersym{2}{m}m!}{k^{\prime}}^{2m+2}\*\left(\ln@@{\left(\frac{1}{k^{\prime}}\right)}+d(m)-\frac{1}{(2m+1)(2m+2)}\right)} | EllipticE(k) = 1 +(1)/(2)*sum((pochhammer((1)/(2), m)*pochhammer((3)/(2), m))/(pochhammer(2, m)*factorial(m))*(sqrt(1 - (k)^(2)))^(2*m + 2)*(ln((1)/(sqrt(1 - (k)^(2))))+ d*(m)-(1)/((2*m + 1)*(2*m + 2))), m = 0..infinity) |
EllipticE[(k)^2] == 1 +Divide[1,2]*Sum[Divide[Pochhammer[Divide[1,2], m]*Pochhammer[Divide[3,2], m],Pochhammer[2, m]*(m)!]*(Sqrt[1 - (k)^(2)])^(2*m + 2)*(Log[Divide[1,Sqrt[1 - (k)^(2)]]]+ d*(m)-Divide[1,(2*m + 1)*(2*m + 2)]), {m, 0, Infinity}, GenerateConditions->None] |
Error | Failure | - | Failed [10 / 10]
{Indeterminate <- {Rule[d, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[k, 1]}Indeterminate <- {Rule[d, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]], Rule[k, 1]} |
| 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 | Failed [30 / 30] 30/30]: [[.4797310429+.5000000000*I <- {d = 1/2*3^(1/2)+1/2*I, m = 1}1.512423114+1.*I <- {d = 1/2*3^(1/2)+1/2*I, m = 2} |
Failed [30 / 30]
{Complex[0.04671834077232884, 0.24999999999999997] <- {Rule[d, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[m, 1]}Complex[0.6463977093312149, 0.49999999999999994] <- {Rule[d, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[m, 2]} |
| 19.12#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d(m+1) = d(m)-\frac{2}{(2m+1)(2m+2)}} | d*(m + 1) = d*(m)-(2)/((2*m + 1)*(2*m + 2)) |
d*(m + 1) == d*(m)-Divide[2,(2*m + 1)*(2*m + 2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 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}, GenerateConditions->None] == (3)^(- 1/ 4)* EllipticF[\[Phi], (k)^2] |
Failure | Aborted | Error | Skipped - Because timed out |
| 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}, GenerateConditions->None] == (3)^(- 1/ 4)* EllipticF[\[Phi], (k)^2] |
Failure | Aborted | Error | Skip - No test values generated |
| 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}, GenerateConditions->None] == Divide[Sign[x],2]*EllipticF[\[Phi], (k)^2] |
Failure | Failure | Error | Skip - No test values generated |
| 19.14.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{\sqrt{(a_{1}+b_{1}t^{2})(a_{2}+b_{2}t^{2})}} = \frac{1}{\sqrt{\gamma-\alpha}}\incellintFk@{\phi}{k}} | int((1)/(sqrt((a[1]+ b[1]*(t)^(2))*(a[2]+ b[2]*(t)^(2)))), t = y..x) = (1)/(sqrt(gamma - alpha))*EllipticF(sin(phi), k) |
Integrate[Divide[1,Sqrt[(Subscript[a, 1]+ Subscript[b, 1]*(t)^(2))*(Subscript[a, 2]+ Subscript[b, 2]*(t)^(2))]], {t, y, x}, GenerateConditions->None] == Divide[1,Sqrt[\[Gamma]- \[Alpha]]]*EllipticF[\[Phi], (k)^2] |
Skipped - Unable to analyze test case: Null | Skipped - Unable to analyze test case: Null | - | - |
| 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 | Failed [300 / 300] 300/300]: [[1.144207228+.1616580578*I <- {U = 1/2*3^(1/2)+1/2*I, alpha = 3/2, gamma = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I}.2329549284-1.570148532*I <- {U = 1/2*3^(1/2)+1/2*I, alpha = 3/2, gamma = 1/2*3^(1/2)+1/2*I, phi = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[1.0397570908067482, -1.0061601508735134] <- {Rule[U, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[α, 1.5], Rule[γ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.7911458419033055, -1.4391726141222814] <- {Rule[U, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[α, 1.5], Rule[γ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.14.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (x^{2}-y^{2})U = x\sqrt{(a_{1}+b_{1}y^{2})(a_{2}+b_{2}y^{2})}+y\sqrt{(a_{1}+b_{1}x^{2})(a_{2}+b_{2}x^{2})}} | ((x)^(2)- (y)^(2))* U = x*sqrt((a[1]+ b[1]*(y)^(2))*(a[2]+ b[2]*(y)^(2)))+ y*sqrt((a[1]+ b[1]*(x)^(2))*(a[2]+ b[2]*(x)^(2))) |
((x)^(2)- (y)^(2))* U == x*Sqrt[(Subscript[a, 1]+ Subscript[b, 1]*(y)^(2))*(Subscript[a, 2]+ Subscript[b, 2]*(y)^(2))]+ y*Sqrt[(Subscript[a, 1]+ Subscript[b, 1]*(x)^(2))*(Subscript[a, 2]+ Subscript[b, 2]*(x)^(2))] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 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 | Failed [300 / 300] 300/300]: [[1.560947444+.1288116535*I <- {alpha = 3/2, gamma = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2, a[1] = 1/2*3^(1/2)+1/2*I, a[2] = 1/2*3^(1/2)+1/2*I}2.678639127-1.794319469*I <- {alpha = 3/2, gamma = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2, a[1] = 1/2*3^(1/2)+1/2*I, a[2] = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[1.3471528039744003, -1.172411794219179] <- {Rule[x, 1.5], Rule[α, 1.5], Rule[γ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.5030688086095803, -1.7852795940180226] <- {Rule[x, 1.5], Rule[α, 1.5], Rule[γ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 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 | Failed [300 / 300] 300/300]: [[.8585159693+.3113806358*I <- {alpha = 3/2, gamma = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, y = -3/2, b[1] = 1/2*3^(1/2)+1/2*I, b[2] = 1/2*3^(1/2)+1/2*I}.2216600130+.2500138214*I <- {alpha = 3/2, gamma = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, y = -3/2, b[1] = 1/2*3^(1/2)+1/2*I, b[2] = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[0.683185473382228, -0.7175596041712626] <- {Rule[y, -1.5], Rule[α, 1.5], Rule[γ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[b, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[b, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.5335538340604822, -1.7418837307419275] <- {Rule[y, -1.5], Rule[α, 1.5], Rule[γ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[b, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[b, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 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 | Manual Skip! | Skipped - Because timed out |
| 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 | Manual Skip! | Skipped - Because timed out |
| 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+x + y*I)), t = 0..infinity) = (1)/(2)*int((1)/(s*(t)), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] == Divide[1,2]*Integrate[Divide[1,s*(t)], {t, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Failed [108 / 108] 108/108]: [[Float(infinity)+1.326265449*I <- {s = -3/2, x = 3/2, y = -3/2}Float(infinity)+Float(infinity)*I <- {s = -3/2, x = 3/2, y = 3/2} |
Failed [108 / 108]
{Complex[52.57956240437182, 0.6784437678906974] <- {Rule[s, -1.5], Rule[x, 1.5], Rule[y, -1.5]}Complex[52.453473067488765, -0.7809212115368181] <- {Rule[s, -1.5], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.16.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{x}{y}{z}{p} = \frac{3}{2}\int_{0}^{\infty}\frac{\diff{t}}{s(t)(t+p)}} | Error |
3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] == Divide[3,2]*Integrate[Divide[1,s*(t)*(t + p)], {t, 0, Infinity}, GenerateConditions->None] |
Missing Macro Error | Failure | - | Skipped - Because timed out |
| 19.16.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRG@{x}{y}{z} = \frac{1}{4\pi}\int_{0}^{2\pi}\!\!\!\!\int_{0}^{\pi}\left(x\sin^{2}@@{\theta}\cos^{2}@@{\phi}+y\sin^{2}@@{\theta}\sin^{2}@@{\phi}+z\cos^{2}@@{\theta}\right)^{\frac{1}{2}}\sin@@{\theta}\diff{\theta}\diff{\phi}} | Error |
Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) == Divide[1,4*Pi]*Integrate[Integrate[(x*(Sin[\[Theta]])^(2)* (Cos[\[Phi]])^(2)+ y*(Sin[\[Theta]])^(2)* (Sin[\[Phi]])^(2)+(x + y*I)*(Cos[\[Theta]])^(2))^(Divide[1,2])* Sin[\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None], {\[Phi], 0, 2*Pi}, GenerateConditions->None] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.16.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s(t) = \sqrt{t+x}\sqrt{t+y}\sqrt{t+z}} | s*(t) = sqrt(t + x)*sqrt(t + y)*sqrt(t +(x + y*I)) |
s*(t) == Sqrt[t + x]*Sqrt[t + y]*Sqrt[t +(x + y*I)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.16.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRD@{x}{y}{z} = \CarlsonsymellintRJ@{x}{y}{z}{z}} | Error |
3*(EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/((x + y*I-y)*(x + y*I-x)^(1/2)) == 3*(x + y*I-x)/(x + y*I-x + y*I)*(EllipticPi[(x + y*I-x + y*I)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Complex[0.37100270206594405, -0.09129381935817127] <- {Rule[x, 1.5], Rule[y, -1.5]}Complex[0.5182279531589904, 0.0513630200054771] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.16.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{x}{y}{z}{z} = \frac{3}{2}\int_{0}^{\infty}\frac{\diff{t}}{s(t)(t+z)}} | Error |
3*(x + y*I-x)/(x + y*I-x + y*I)*(EllipticPi[(x + y*I-x + y*I)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] == Divide[3,2]*Integrate[Divide[1,s*(t)*(t +(x + y*I))], {t, 0, Infinity}, GenerateConditions->None] |
Missing Macro Error | Failure | - | Skipped - Because timed out |
| 19.16.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x}{y} = \CarlsonsymellintRF@{x}{y}{y}} | Error |
1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)] == EllipticF[ArcCos[Sqrt[x/y]],(y-y)/(y-x)]/Sqrt[y-x] |
Missing Macro Error | Failure | - | Failed [3 / 18]
{Indeterminate <- {Rule[x, 1.5], Rule[y, 1.5]}Indeterminate <- {Rule[x, 0.5], Rule[y, 0.5]} |
| 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 | Failed [60 / 60] 60/60]: [[-2.359812877+.7993130071*I <- {c = -3/2, phi = 1/2*3^(1/2)+1/2*I}-1.296085040-.8173084059*I <- {c = -3/2, phi = -1/2+1/2*I*3^(1/2)} |
Failed [60 / 60]
{Complex[-3.841312467237177, 3.4490957612740374] <- {Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.17530792640393877, -3.4502399957777015] <- {Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.18.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\CarlsonsymellintRF@{x}{y}{z}}{z} = -\tfrac{1}{6}\CarlsonsymellintRD@{x}{y}{z}} | Error |
(D[EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x], {temp, 1}]/.temp-> (x + y*I)) == -Divide[1,6]*3*(EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/((x + y*I-y)*(x + y*I-x)^(1/2)) |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Complex[0.03790163875178684, -0.07848225754688502] <- {Rule[x, 1.5], Rule[y, -1.5]}Complex[0.07302626282106058, 0.09607801553820669] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.18.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{x}\CarlsonsymellintRG@{x+a}{x+b}{x+c} = \tfrac{1}{2}\CarlsonsymellintRF@{x+a}{x+b}{x+c}} | Error |
D[Sqrt[x + c-x + a]*(EllipticE[ArcCos[Sqrt[x + a/x + c]],(x + c-x + b)/(x + c-x + a)]+(Cot[ArcCos[Sqrt[x + a/x + c]]])^2*EllipticF[ArcCos[Sqrt[x + a/x + c]],(x + c-x + b)/(x + c-x + a)]+Cot[ArcCos[Sqrt[x + a/x + c]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x + a/x + c]]]^2]), x] == Divide[1,2]*EllipticF[ArcCos[Sqrt[x + a/x + c]],(x + c-x + b)/(x + c-x + a)]/Sqrt[x + c-x + a] |
Missing Macro Error | Aborted | - | Failed [300 / 300]
{Plus[Complex[0.4534498410585545, 0.2544306388611797], Times[Complex[0.0, 1.7320508075688772], Plus[Complex[-0.5166444818917079, -0.6544984694978735], Times[Complex[0.0, 0.5892556509887895], Power[k, 2], Power[Plus[1.0, Times[-2.0, Power[k, 2]]], Rational[-1, 2]]], Times[Complex[0.0, -0.29462782549439476], Power[Plus[1.0, Times[-2.0, Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[x, 1.5]}Plus[Complex[0.4534498410585545, 0.1389138883676965], Times[Complex[0.0, 1.7320508075688772], Plus[Complex[-1.7435577900831345, -0.43982297150257077], Times[Complex[0.0, 3.1304951684997055], Power[k, 2], Power[Plus[1.0, Times[-5.0, Power[k, 2]]], Rational[-1, 2]]], Times[Complex[0.0, -0.15652475842498526], Power[Plus[1.0, Times[-5.0, Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[x, 0.5]} |
| 19.18.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(x\pderiv{}{x}+y\pderiv{}{y}+z\pderiv{}{z}\right)\CarlsonsymellintRF@{x}{y}{z} = -\tfrac{1}{2}\CarlsonsymellintRF@{x}{y}{z}} | (x*diff(+ y*diff(+subs( temp=(x + y*I), diff( temp, temp$(1) ) ), y), x))* 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) = -(1)/(2)*0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) |
(x*D[+ y*D[+(D[temp, {temp, 1}]/.temp-> (x + y*I)), y], x])* EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] == -Divide[1,2]*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] |
Aborted | Failure | Failed [18 / 18] 18/18]: [[-.8633499928+.6631327246*I <- {x = 3/2, y = -3/2}Float(infinity)+Float(infinity)*I <- {x = 3/2, y = 3/2} |
Failed [18 / 18]
{Complex[-0.08107235486578032, 0.3392218839453487] <- {Rule[x, 1.5], Rule[y, -1.5]}Complex[-0.14411702330731, -0.3904606057684091] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.18.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{w}{x} = \pderiv[2]{w}{y}+\frac{1}{y}\pderiv{w}{y}} | diff(w, [x$(2)]) = diff(w, [y$(2)])+(1)/(y)*diff(w, y) |
D[w, {x, 2}] == D[w, {y, 2}]+Divide[1,y]*D[w, y] |
Successful | Successful | - | Successful [Tested: 180] |
| 19.18.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{W}{t} = \pderiv[2]{W}{x}+\pderiv[2]{W}{y}} | diff(W, [t$(2)]) = diff(W, [x$(2)])+ diff(W, [y$(2)]) |
D[W, {t, 2}] == D[W, {x, 2}]+ D[W, {y, 2}] |
Successful | Successful | - | Successful [Tested: 300] |
| 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 | - | Successful [Tested: 180] |
| 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)])+ subs( temp=(x + y*I), diff( U, temp$(2) ) ) = 0 |
D[U, {x, 2}]+ D[U, {y, 2}]+ (D[U, {temp, 2}]/.temp-> (x + y*I)) == 0 |
Successful | Successful | - | Successful [Tested: 180] |
| 19.19#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A = \frac{1}{n}\sum_{j=1}^{n}z_{j}} | A = (1)/(n)*sum(z[j], j = 1..n) |
A == Divide[1,n]*Sum[Subscript[z, j], {j, 1, n}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.19#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Z_{j} = 1-(z_{j}/A)} | Z[j] = 1 -(z[j]/ A) |
Subscript[Z, j] == 1 -(Subscript[z, j]/ A) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.19#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle E_{1}(\mathbf{Z}) = 0} | E[1]*(Z) = 0 |
Subscript[E, 1]*(Z) == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 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) |
EllipticF[ArcCos[Sqrt[x/x]],(x-x)/(x-x)]/Sqrt[x-x] == (x)^(- 1/ 2) |
Failure | Failure | Successful [Tested: 3] | Failed [3 / 3]
{Indeterminate <- {Rule[x, 1.5]}Indeterminate <- {Rule[x, 0.5]} |
| 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*(x + y*I))), t = 0..infinity) = (lambda)^(- 1/ 2)* 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[\[Lambda]*x/\[Lambda]*(x + y*I)]],(\[Lambda]*(x + y*I)-\[Lambda]*y)/(\[Lambda]*(x + y*I)-\[Lambda]*x)]/Sqrt[\[Lambda]*(x + y*I)-\[Lambda]*x] == \[Lambda]^(- 1/ 2)* EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] |
Aborted | Failure | Skipped - Because timed out | Failed [180 / 180]
{Complex[-0.15259412278903736, 0.06775202977854555] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.05999241929777854, 0.15580825868890358] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.20#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{y} = \CarlsonellintRC@{x}{y}} | Error |
EllipticF[ArcCos[Sqrt[x/y]],(y-y)/(y-x)]/Sqrt[y-x] == 1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)] |
Missing Macro Error | Failure | - | Failed [3 / 18]
{Indeterminate <- {Rule[x, 1.5], Rule[y, 1.5]}Indeterminate <- {Rule[x, 0.5], Rule[y, 0.5]} |
| 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) |
EllipticF[ArcCos[Sqrt[0/y]],(y-y)/(y-0)]/Sqrt[y-0] == Divide[1,2]*Pi*(y)^(- 1/ 2) |
Failure | Successful | Failed [3 / 6] 3/6]: [[2.565099660*I <- {y = -3/2}4.442882938*I <- {y = -1/2} |
Successful [Tested: 6] |
| 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 |
EllipticF[ArcCos[Sqrt[0/z]],(z-0)/(z-0)]/Sqrt[z-0] == Infinity |
Failure | Failure | Skipped - Because timed out | Failed [7 / 7]
{Indeterminate <- {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Indeterminate <- {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 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) |
Integrate[Divide[1,Sqrt[1 - (t)^(4)]], {t, 0, 1}, GenerateConditions->None] == EllipticF[ArcCos[Sqrt[0/2]],(2-1)/(2-0)]/Sqrt[2-0] |
Failure | Successful | Successful [Tested: 0] | Successful [Tested: 1] |
| 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)) |
EllipticF[ArcCos[Sqrt[0/2]],(2-1)/(2-0)]/Sqrt[2-0] == Divide[(Gamma[Divide[1,4]])^(2),4*(2*Pi)^(1/ 2)] |
Successful | Failure | Skip - symbolical successful subtest | Successful [Tested: 1] |
| 19.20.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\left(\EulerGamma@{\frac{1}{4}}\right)^{2}}{4(2\pi)^{1/2}} = 1.31102\;87771\;46059\;90523\;\dots} | ((GAMMA((1)/(4)))^(2))/(4*(2*Pi)^(1/ 2)) = 1.31102877714605990523 |
Divide[(Gamma[Divide[1,4]])^(2),4*(2*Pi)^(1/ 2)] == 1.31102877714605990523 |
Failure | Successful | Successful [Tested: 0] | Successful [Tested: 1] |
| 19.20#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRG@{x}{x}{x} = x^{1/2}} | Error |
Sqrt[x-x]*(EllipticE[ArcCos[Sqrt[x/x]],(x-x)/(x-x)]+(Cot[ArcCos[Sqrt[x/x]]])^2*EllipticF[ArcCos[Sqrt[x/x]],(x-x)/(x-x)]+Cot[ArcCos[Sqrt[x/x]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x]]]^2]) == (x)^(1/ 2) |
Missing Macro Error | Failure | - | Failed [3 / 3]
{Indeterminate <- {Rule[x, 1.5]}Indeterminate <- {Rule[x, 0.5]} |
| 19.20#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRG@{\lambda x}{\lambda y}{\lambda z} = \lambda^{1/2}\CarlsonsymellintRG@{x}{y}{z}} | Error |
Sqrt[\[Lambda]*(x + y*I)-\[Lambda]*x]*(EllipticE[ArcCos[Sqrt[\[Lambda]*x/\[Lambda]*(x + y*I)]],(\[Lambda]*(x + y*I)-\[Lambda]*y)/(\[Lambda]*(x + y*I)-\[Lambda]*x)]+(Cot[ArcCos[Sqrt[\[Lambda]*x/\[Lambda]*(x + y*I)]]])^2*EllipticF[ArcCos[Sqrt[\[Lambda]*x/\[Lambda]*(x + y*I)]],(\[Lambda]*(x + y*I)-\[Lambda]*y)/(\[Lambda]*(x + y*I)-\[Lambda]*x)]+Cot[ArcCos[Sqrt[\[Lambda]*x/\[Lambda]*(x + y*I)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[\[Lambda]*x/\[Lambda]*(x + y*I)]]]^2]) == \[Lambda]^(1/ 2)* Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) |
Missing Macro Error | Aborted | - | Failed [180 / 180] {Plus[Times[Complex[-0.75, 0.4330127018922193], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]], Times[Complex[0.75, -0.43301270189221935], Plus[Complex[0.469094970899074, 0.7900882534928779], Times[Complex[0.1542171038749957, -1.1011185950707625], Power[Plus[1.0, Times[Complex[1.25, -2.25], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Plus[Times[Complex[-0.8365163037378078, -0.22414386804201336], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]], Times[Complex[0.8365163037378078, 0.22414386804201325], Plus[Complex[0.46909497089907387, 0.7900882534928779], Times[Complex[0.1542171038749957, -1.10
|
| 19.20#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRG@{0}{y}{y} = \tfrac{1}{4}\pi y^{1/2}} | Error |
Sqrt[y-0]*(EllipticE[ArcCos[Sqrt[0/y]],(y-y)/(y-0)]+(Cot[ArcCos[Sqrt[0/y]]])^2*EllipticF[ArcCos[Sqrt[0/y]],(y-y)/(y-0)]+Cot[ArcCos[Sqrt[0/y]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/y]]]^2]) == Divide[1,4]*Pi*(y)^(1/ 2) |
Missing Macro Error | Failure | - | Failed [6 / 6]
{Complex[0.0, 0.961912372621398] <- {Rule[y, -1.5]}0.961912372621398 <- {Rule[y, 1.5]} |
| 19.20#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRG@{0}{0}{z} = \tfrac{1}{2}z^{1/2}} | Error |
Sqrt[z-0]*(EllipticE[ArcCos[Sqrt[0/z]],(z-0)/(z-0)]+(Cot[ArcCos[Sqrt[0/z]]])^2*EllipticF[ArcCos[Sqrt[0/z]],(z-0)/(z-0)]+Cot[ArcCos[Sqrt[0/z]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/z]]]^2]) == Divide[1,2]*(z)^(1/ 2) |
Missing Macro Error | Failure | - | Failed [7 / 7]
{Indeterminate <- {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Indeterminate <- {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.20.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRG@{x}{y}{y} = y\CarlsonellintRC@{x}{y}+\sqrt{x}} | Error |
2*Sqrt[y-x]*(EllipticE[ArcCos[Sqrt[x/y]],(y-y)/(y-x)]+(Cot[ArcCos[Sqrt[x/y]]])^2*EllipticF[ArcCos[Sqrt[x/y]],(y-y)/(y-x)]+Cot[ArcCos[Sqrt[x/y]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/y]]]^2]) == y*1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)]+Sqrt[x] |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Plus[Complex[-1.988036787975128, -1.360349523175663], Times[Complex[0.0, 3.4641016151377544], Plus[Complex[0.7853981633974483, -0.44068679350977147], Times[Complex[0.0, 0.7071067811865475], Power[Plus[1.0, Times[-2.0, Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, -1.5]}Indeterminate <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.20#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{x}{x}{x}{x} = x^{-3/2}} | Error |
3*(x-x)/(x-x)*(EllipticPi[(x-x)/(x-x),ArcCos[Sqrt[x/x]],(x-x)/(x-x)]-EllipticF[ArcCos[Sqrt[x/x]],(x-x)/(x-x)])/Sqrt[x-x] == (x)^(- 3/ 2) |
Missing Macro Error | Failure | - | Failed [3 / 3]
{Indeterminate <- {Rule[x, 1.5]}Indeterminate <- {Rule[x, 0.5]} |
| 19.20#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{\lambda x}{\lambda y}{\lambda z}{\lambda p} = \lambda^{-3/2}\CarlsonsymellintRJ@{x}{y}{z}{p}} | Error |
3*(\[Lambda]*(x + y*I)-\[Lambda]*x)/(\[Lambda]*(x + y*I)-\[Lambda]*p)*(EllipticPi[(\[Lambda]*(x + y*I)-\[Lambda]*p)/(\[Lambda]*(x + y*I)-\[Lambda]*x),ArcCos[Sqrt[\[Lambda]*x/\[Lambda]*(x + y*I)]],(\[Lambda]*(x + y*I)-\[Lambda]*y)/(\[Lambda]*(x + y*I)-\[Lambda]*x)]-EllipticF[ArcCos[Sqrt[\[Lambda]*x/\[Lambda]*(x + y*I)]],(\[Lambda]*(x + y*I)-\[Lambda]*y)/(\[Lambda]*(x + y*I)-\[Lambda]*x)])/Sqrt[\[Lambda]*(x + y*I)-\[Lambda]*x] == \[Lambda]^(- 3/ 2)* 3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Complex[0.8261798979421457, -0.5239696989052641] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.5256524914787406, -1.066611458671583] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.20#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{x}{y}{z}{z} = \CarlsonsymellintRD@{x}{y}{z}} | Error |
3*(x + y*I-x)/(x + y*I-x + y*I)*(EllipticPi[(x + y*I-x + y*I)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] == 3*(EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/((x + y*I-y)*(x + y*I-x)^(1/2)) |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Complex[-0.37100270206594405, 0.09129381935817127] <- {Rule[x, 1.5], Rule[y, -1.5]}Complex[-0.5182279531589904, -0.0513630200054771] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.20#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{0}{0}{z}{p} = \infty} | Error |
3*(z-0)/(z-p)*(EllipticPi[(z-p)/(z-0),ArcCos[Sqrt[0/z]],(z-0)/(z-0)]-EllipticF[ArcCos[Sqrt[0/z]],(z-0)/(z-0)])/Sqrt[z-0] == Infinity |
Missing Macro Error | Failure | - | Failed [70 / 70]
{Indeterminate <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Indeterminate <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.20#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{x}{x}{x}{p} = \CarlsonsymellintRD@{p}{p}{x}} | Error |
3*(x-x)/(x-p)*(EllipticPi[(x-p)/(x-x),ArcCos[Sqrt[x/x]],(x-x)/(x-x)]-EllipticF[ArcCos[Sqrt[x/x]],(x-x)/(x-x)])/Sqrt[x-x] == 3*(EllipticF[ArcCos[Sqrt[p/x]],(x-p)/(x-p)]-EllipticE[ArcCos[Sqrt[p/x]],(x-p)/(x-p)])/((x-p)*(x-p)^(1/2)) |
Missing Macro Error | Failure | - | Failed [27 / 27]
{Indeterminate <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5]}Indeterminate <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 0.5]} |
| 19.20#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRD@{p}{p}{x} = \frac{3}{x-p}\left(\CarlsonellintRC@{x}{p}-\frac{1}{\sqrt{x}}\right)} | Error |
3*(EllipticF[ArcCos[Sqrt[p/x]],(x-p)/(x-p)]-EllipticE[ArcCos[Sqrt[p/x]],(x-p)/(x-p)])/((x-p)*(x-p)^(1/2)) == Divide[3,x - p]*(1/Sqrt[p]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(p)]-Divide[1,Sqrt[x]]) |
Missing Macro Error | Failure | - | Failed [9 / 27]
{Complex[1.0177225554447191, 2.220446049250313*^-16] <- {Rule[p, -1.5], Rule[x, 1.5]}Complex[1.1652542988181402, 6.661338147750939*^-16] <- {Rule[p, -1.5], Rule[x, 0.5]} |
| 19.20#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{0}{y}{y}{p} = \frac{3\pi}{2(y\sqrt{p}+p\sqrt{y})}} | Error |
3*(y-0)/(y-p)*(EllipticPi[(y-p)/(y-0),ArcCos[Sqrt[0/y]],(y-y)/(y-0)]-EllipticF[ArcCos[Sqrt[0/y]],(y-y)/(y-0)])/Sqrt[y-0] == Divide[3*Pi,2*(y*Sqrt[p]+ p*Sqrt[y])] |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Complex[-0.6412749150809316, 3.2063745754046598] <- {Rule[p, 1.5], Rule[y, -1.5]}Indeterminate <- {Rule[p, 1.5], Rule[y, 1.5]} |
| 19.20#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{0}{y}{y}{-q} = \frac{-3\pi}{2\sqrt{y}(y+q)}} | Error |
3*(y-0)/(y-- q)*(EllipticPi[(y-- q)/(y-0),ArcCos[Sqrt[0/y]],(y-y)/(y-0)]-EllipticF[ArcCos[Sqrt[0/y]],(y-y)/(y-0)])/Sqrt[y-0] == Divide[- 3*Pi,2*Sqrt[y]*(y + q)] |
Missing Macro Error | Failure | - | Failed [18 / 18]
{DirectedInfinity[] <- {Rule[q, 1.5], Rule[y, -1.5]}Plus[1.282549830161864, Times[2.449489742783178, Plus[-1.5707963267948966, Times[1.5707963267948966, Power[Plus[1.0, Times[-1.0, Decrement[1.5]]], Rational[-1, 2]]]], Power[Decrement[1.5], -1]]] <- {Rule[q, 1.5], Rule[y, 1.5]} |
| 19.20#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{x}{y}{y}{p} = \frac{3}{p-y}(\CarlsonellintRC@{x}{y}-\CarlsonellintRC@{x}{p})} | Error |
3*(y-x)/(y-p)*(EllipticPi[(y-p)/(y-x),ArcCos[Sqrt[x/y]],(y-y)/(y-x)]-EllipticF[ArcCos[Sqrt[x/y]],(y-y)/(y-x)])/Sqrt[y-x] == Divide[3,p - y]*(1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)]- 1/Sqrt[p]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(p)]) |
Missing Macro Error | Aborted | - | Failed [157 / 162]
{Complex[0.40904124998304914, 6.107600792054881] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}Indeterminate <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.20#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{x}{y}{y}{y} = \CarlsonsymellintRD@{x}{y}{y}} | Error |
3*(y-x)/(y-y)*(EllipticPi[(y-y)/(y-x),ArcCos[Sqrt[x/y]],(y-y)/(y-x)]-EllipticF[ArcCos[Sqrt[x/y]],(y-y)/(y-x)])/Sqrt[y-x] == 3*(EllipticF[ArcCos[Sqrt[x/y]],(y-y)/(y-x)]-EllipticE[ArcCos[Sqrt[x/y]],(y-y)/(y-x)])/((y-y)*(y-x)^(1/2)) |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Indeterminate <- {Rule[x, 1.5], Rule[y, -1.5]}Indeterminate <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.20.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{0}{y}{z}{+\sqrt{yz}} = +\frac{3}{2\sqrt{yz}}\CarlsonsymellintRF@{0}{y}{z}} | Error |
3*(x + y*I-0)/(x + y*I-+Sqrt[y*(x + y*I)])*(EllipticPi[(x + y*I-+Sqrt[y*(x + y*I)])/(x + y*I-0),ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/Sqrt[x + y*I-0] == +Divide[3,2*Sqrt[y*(x + y*I)]]*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0] |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Complex[-0.9141259292931587, -0.9706303463287326] <- {Rule[x, 1.5], Rule[y, -1.5]}Complex[-4.407772019377616, 0.7576222483343515] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.20.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{0}{y}{z}{-\sqrt{yz}} = -\frac{3}{2\sqrt{yz}}\CarlsonsymellintRF@{0}{y}{z}} | Error |
3*(x + y*I-0)/(x + y*I--Sqrt[y*(x + y*I)])*(EllipticPi[(x + y*I--Sqrt[y*(x + y*I)])/(x + y*I-0),ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/Sqrt[x + y*I-0] == -Divide[3,2*Sqrt[y*(x + y*I)]]*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0] |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Complex[0.1671030668705316, -0.09828926199489627] <- {Rule[x, 1.5], Rule[y, -1.5]}Complex[-0.7387931095854892, 1.0731895314108653] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.20#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to 0+}\sqrt{p}\CarlsonsymellintRJ@{0}{y}{z}{p} = \frac{3\pi}{2\sqrt{yz}}} | Error |
Limit[Sqrt[p]*3*(x + y*I-0)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-0),ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/Sqrt[x + y*I-0], p -> 0, Direction -> "FromAbove", GenerateConditions->None] == Divide[3*Pi,2*Sqrt[y*(x + y*I)]] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.20#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to 0-}\CarlsonsymellintRJ@{0}{y}{z}{p} = {-\CarlsonsymellintRD@{0}{y}{z}-\CarlsonsymellintRD@{0}{z}{y}}} | Error |
Limit[3*(x + y*I-0)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-0),ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/Sqrt[x + y*I-0], p -> 0, Direction -> "FromBelow", GenerateConditions->None] == - 3*(EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/((x + y*I-y)*(x + y*I-0)^(1/2))- 3*(EllipticF[ArcCos[Sqrt[0/y]],(y-x + y*I)/(y-0)]-EllipticE[ArcCos[Sqrt[0/y]],(y-x + y*I)/(y-0)])/((y-x + y*I)*(y-0)^(1/2)) |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.20#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {-\CarlsonsymellintRD@{0}{y}{z}-\CarlsonsymellintRD@{0}{z}{y}} = \frac{-6}{yz}\CarlsonsymellintRG@{0}{y}{z}} | Error |
- 3*(EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/((x + y*I-y)*(x + y*I-0)^(1/2))- 3*(EllipticF[ArcCos[Sqrt[0/y]],(y-x + y*I)/(y-0)]-EllipticE[ArcCos[Sqrt[0/y]],(y-x + y*I)/(y-0)])/((y-x + y*I)*(y-0)^(1/2)) == Divide[- 6,y*(x + y*I)]*Sqrt[x + y*I-0]*(EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]+(Cot[ArcCos[Sqrt[0/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]+Cot[ArcCos[Sqrt[0/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/x + y*I]]]^2]) |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Plus[Complex[1.5111033799217843, -0.47027281525563985], Times[Complex[-2.537302274660022, -1.050985014004285], Plus[Complex[1.465481142300126, -0.24396122198922798], Times[Complex[0.2643318009908678, -0.8730286325904596], Power[Plus[1.0, Times[Complex[-1.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, -1.5]}Plus[Complex[-0.13967540286775149, -0.9399293972008751], Times[Complex[2.537302274660022, -1.050985014004285], Plus[Complex[1.0084590214609772, 0.7147093671486319], Times[Complex[0.2643318009908678, 0.8730286325904596], Power[Plus[1.0, Times[Complex[-1.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.20.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to+\infty}p\CarlsonsymellintRJ@{x}{y}{z}{p} = 3\CarlsonsymellintRF@{x}{y}{z}} | Error |
Limit[p*3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x], p -> + Infinity, GenerateConditions->None] == 3*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.20.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to-\infty}p\CarlsonsymellintRJ@{x}{y}{z}{p} = 3\CarlsonsymellintRF@{x}{y}{z}} | Error |
Limit[p*3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x], p -> - Infinity, GenerateConditions->None] == 3*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.20.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2(p-x)\CarlsonsymellintRJ@{x}{y}{z}{p} = 3\CarlsonsymellintRF@{x}{y}{z}-3\sqrt{x}\CarlsonellintRC@{yz}{p^{2}}} | Error |
2*(p - x)* 3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] == 3*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x]- 3*Sqrt[x]*1/Sqrt[(p)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(y*(x + y*I))/((p)^(2))] |
Missing Macro Error | Aborted | - | Failed [180 / 180]
{Complex[3.989482635019833, -4.816521080718802] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}Complex[5.152296981249878, -0.7434346709776987] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.20.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (q+z)\CarlsonsymellintRJ@{x}{y}{z}{-q} = (p-z)\CarlsonsymellintRJ@{x}{y}{z}{p}-3\CarlsonsymellintRF@{x}{y}{z}+3\left(\frac{xyz}{xy+pq}\right)^{1/2}\CarlsonellintRC@{xy+pq}{pq}} | Error |
(q +(x + y*I))* 3*(x + y*I-x)/(x + y*I-- q)*(EllipticPi[(x + y*I-- q)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] == (p -(x + y*I))* 3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x]- 3*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x]+ 3*(Divide[x*y*(x + y*I),x*y + p*q])^(1/ 2)* 1/Sqrt[p*q]*Hypergeometric2F1[1/2,1/2,3/2,1-(x*y + p*q)/(p*q)] |
Missing Macro Error | Aborted | - | Failed [300 / 300]
{Complex[-3.4116287326863786, 8.252883937385896] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}Complex[-8.900891250450524, -2.579723477019983] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.20#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q > 0} | q > 0 |
q > 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.20#Ex22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = \frac{z(x+y+q)-xy}{z+q}} | p = ((x + y*I)*(x + y + q)- x*y)/((x + y*I)+ q) |
p == Divide[(x + y*I)*(x + y + q)- x*y,(x + y*I)+ q] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.20#Ex23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = wy+(1-w)z} | p = w*y +(1 - w)*(x + y*I) |
p == w*y +(1 - w)*(x + y*I) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.20#Ex24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \frac{z-x}{z+q}} | w = ((x + y*I)- x)/((x + y*I)+ q) |
w == Divide[(x + y*I)- x,(x + y*I)+ q] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.20#Ex25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < w} | 0 < w |
0 < w |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.20.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (q+z)\CarlsonsymellintRJ@{0}{y}{z}{-q} = (p-z)\CarlsonsymellintRJ@{0}{y}{z}{p}-3\CarlsonsymellintRF@{0}{y}{z}} | Error |
(q +(x + y*I))* 3*(x + y*I-0)/(x + y*I-- q)*(EllipticPi[(x + y*I-- q)/(x + y*I-0),ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/Sqrt[x + y*I-0] == (p -(x + y*I))* 3*(x + y*I-0)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-0),ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/Sqrt[x + y*I-0]- 3*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Complex[-3.556352843352318, 3.1308549992075583] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}Complex[-7.694083210877473, -5.44447388199589] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.20#Ex26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRD@{x}{x}{x} = x^{-3/2}} | Error |
3*(EllipticF[ArcCos[Sqrt[x/x]],(x-x)/(x-x)]-EllipticE[ArcCos[Sqrt[x/x]],(x-x)/(x-x)])/((x-x)*(x-x)^(1/2)) == (x)^(- 3/ 2) |
Missing Macro Error | Failure | - | Failed [3 / 3]
{Indeterminate <- {Rule[x, 1.5]}Indeterminate <- {Rule[x, 0.5]} |
| 19.20#Ex27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRD@{\lambda x}{\lambda y}{\lambda z} = \lambda^{-3/2}\CarlsonsymellintRD@{x}{y}{z}} | Error |
3*(EllipticF[ArcCos[Sqrt[\[Lambda]*x/\[Lambda]*(x + y*I)]],(\[Lambda]*(x + y*I)-\[Lambda]*y)/(\[Lambda]*(x + y*I)-\[Lambda]*x)]-EllipticE[ArcCos[Sqrt[\[Lambda]*x/\[Lambda]*(x + y*I)]],(\[Lambda]*(x + y*I)-\[Lambda]*y)/(\[Lambda]*(x + y*I)-\[Lambda]*x)])/((\[Lambda]*(x + y*I)-\[Lambda]*y)*(\[Lambda]*(x + y*I)-\[Lambda]*x)^(1/2)) == \[Lambda]^(- 3/ 2)* 3*(EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/((x + y*I-y)*(x + y*I-x)^(1/2)) |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Complex[1.0149076549010991, -0.8161311339182895] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.2947399441897933, -0.14055622592761496] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.20#Ex29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRD@{0}{0}{z} = \infty} | Error |
3*(EllipticF[ArcCos[Sqrt[0/z]],(z-0)/(z-0)]-EllipticE[ArcCos[Sqrt[0/z]],(z-0)/(z-0)])/((z-0)*(z-0)^(1/2)) == Infinity |
Missing Macro Error | Failure | - | Failed [7 / 7]
{Indeterminate <- {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Indeterminate <- {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.20.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRD@{x}{y}{y} = \frac{3}{2(y-x)}\left(\CarlsonellintRC@{x}{y}-\frac{\sqrt{x}}{y}\right)} | Error |
3*(EllipticF[ArcCos[Sqrt[x/y]],(y-y)/(y-x)]-EllipticE[ArcCos[Sqrt[x/y]],(y-y)/(y-x)])/((y-y)*(y-x)^(1/2)) == Divide[3,2*(y - x)]*(1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)]-Divide[Sqrt[x],y]) |
Missing Macro Error | Failure | - | Failed [15 / 15]
{Indeterminate <- {Rule[x, 1.5], Rule[y, -1.5]}Indeterminate <- {Rule[x, 1.5], Rule[y, -0.5]} |
| 19.20.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRD@{x}{x}{z} = \frac{3}{z-x}\left(\CarlsonellintRC@{z}{x}-\frac{1}{\sqrt{z}}\right)} | Error |
3*(EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-x)/(x + y*I-x)]-EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-x)/(x + y*I-x)])/((x + y*I-x)*(x + y*I-x)^(1/2)) == Divide[3,(x + y*I)- x]*(1/Sqrt[x]*Hypergeometric2F1[1/2,1/2,3/2,1-(x + y*I)/(x)]-Divide[1,Sqrt[x + y*I]]) |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Complex[0.13486015646372063, -0.8506635330353051] <- {Rule[x, 1.5], Rule[y, -1.5]}Complex[0.13486015646372096, 0.8506635330353054] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.20.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}\frac{t^{2}\diff{t}}{\sqrt{1-t^{4}}} = \tfrac{1}{3}\CarlsonsymellintRD@{0}{2}{1}} | Error |
Integrate[Divide[(t)^(2),Sqrt[1 - (t)^(4)]], {t, 0, 1}, GenerateConditions->None] == Divide[1,3]*3*(EllipticF[ArcCos[Sqrt[0/1]],(1-2)/(1-0)]-EllipticE[ArcCos[Sqrt[0/1]],(1-2)/(1-0)])/((1-2)*(1-0)^(1/2)) |
Missing Macro Error | Successful | Skip - symbolical successful subtest | Successful [Tested: 1] |
| 19.20.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{3}\CarlsonsymellintRD@{0}{2}{1} = \frac{\left(\EulerGamma@{\frac{3}{4}}\right)^{2}}{(2\pi)^{1/2}}} | Error |
Divide[1,3]*3*(EllipticF[ArcCos[Sqrt[0/1]],(1-2)/(1-0)]-EllipticE[ArcCos[Sqrt[0/1]],(1-2)/(1-0)])/((1-2)*(1-0)^(1/2)) == Divide[(Gamma[Divide[3,4]])^(2),(2*Pi)^(1/ 2)] |
Missing Macro Error | Successful | Skip - symbolical successful subtest | Successful [Tested: 1] |
| 19.20.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\left(\EulerGamma@{\frac{3}{4}}\right)^{2}}{(2\pi)^{1/2}} = 0.59907\;01173\;67796\;10371\dots} | ((GAMMA((3)/(4)))^(2))/((2*Pi)^(1/ 2)) = 0.59907011736779610371 |
Divide[(Gamma[Divide[3,4]])^(2),(2*Pi)^(1/ 2)] == 0.59907011736779610371 |
Failure | Successful | Successful [Tested: 0] | Successful [Tested: 1] |
| 19.21.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{0}{z+1}{z}\CarlsonsymellintRD@{0}{z+1}{1}+\CarlsonsymellintRD@{0}{z+1}{z}\CarlsonsymellintRF@{0}{z+1}{1} = 3\pi/(2z)} | Error |
EllipticF[ArcCos[Sqrt[0/z]],(z-z + 1)/(z-0)]/Sqrt[z-0]*3*(EllipticF[ArcCos[Sqrt[0/1]],(1-z + 1)/(1-0)]-EllipticE[ArcCos[Sqrt[0/1]],(1-z + 1)/(1-0)])/((1-z + 1)*(1-0)^(1/2))+ 3*(EllipticF[ArcCos[Sqrt[0/z]],(z-z + 1)/(z-0)]-EllipticE[ArcCos[Sqrt[0/z]],(z-z + 1)/(z-0)])/((z-z + 1)*(z-0)^(1/2))*EllipticF[ArcCos[Sqrt[0/1]],(1-z + 1)/(1-0)]/Sqrt[1-0] == 3*Pi/(2*z) |
Missing Macro Error | Failure | - | Failed [7 / 7]
{Complex[-18.895019118218656, -13.266297761785948] <- {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-2.405668177707024, 11.584123712813607] <- {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.21.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 3\CarlsonsymellintRF@{0}{y}{z} = z\CarlsonsymellintRD@{0}{y}{z}+y\CarlsonsymellintRD@{0}{z}{y}} | Error |
3*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0] == (x + y*I)* 3*(EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/((x + y*I-y)*(x + y*I-0)^(1/2))+ y*3*(EllipticF[ArcCos[Sqrt[0/y]],(y-x + y*I)/(y-0)]-EllipticE[ArcCos[Sqrt[0/y]],(y-x + y*I)/(y-0)])/((y-x + y*I)*(y-0)^(1/2)) |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Complex[-0.11482200178525792, 3.077769310376559] <- {Rule[x, 1.5], Rule[y, -1.5]}Complex[0.9930498831204495, -3.2293137034341144] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.21.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 6\CarlsonsymellintRG@{0}{y}{z} = yz(\CarlsonsymellintRD@{0}{y}{z}+\CarlsonsymellintRD@{0}{z}{y})} | Error |
6*Sqrt[x + y*I-0]*(EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]+(Cot[ArcCos[Sqrt[0/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]+Cot[ArcCos[Sqrt[0/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/x + y*I]]]^2]) == y*(x + y*I)*(3*(EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/((x + y*I-y)*(x + y*I-0)^(1/2))+ 3*(EllipticF[ArcCos[Sqrt[0/y]],(y-x + y*I)/(y-0)]-EllipticE[ArcCos[Sqrt[0/y]],(y-x + y*I)/(y-0)])/((y-x + y*I)*(y-0)^(1/2))) |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Plus[Complex[-2.3418687704988255, 4.458096439149204], Times[Complex[8.07364639949469, -3.344213836475408], Plus[Complex[1.465481142300126, -0.24396122198922798], Times[Complex[0.2643318009908678, -0.8730286325904596], Power[Plus[1.0, Times[Complex[-1.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, -1.5]}Plus[Complex[1.800571487249528, -2.4291108001544095], Times[Complex[8.07364639949469, 3.344213836475408], Plus[Complex[1.0084590214609772, 0.7147093671486319], Times[Complex[0.2643318009908678, 0.8730286325904596], Power[Plus[1.0, Times[Complex[-1.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.21.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle yz(\CarlsonsymellintRD@{0}{y}{z}+\CarlsonsymellintRD@{0}{z}{y}) = 3z\CarlsonsymellintRF@{0}{y}{z}+z(y-z)\CarlsonsymellintRD@{0}{y}{z}} | Error |
y*(x + y*I)*(3*(EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/((x + y*I-y)*(x + y*I-0)^(1/2))+ 3*(EllipticF[ArcCos[Sqrt[0/y]],(y-x + y*I)/(y-0)]-EllipticE[ArcCos[Sqrt[0/y]],(y-x + y*I)/(y-0)])/((y-x + y*I)*(y-0)^(1/2))) == 3*(x + y*I)* EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0]+(x + y*I)*(y -(x + y*I))* 3*(EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/((x + y*I-y)*(x + y*I-0)^(1/2)) |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Complex[-4.444420962886951, -4.788886968242726] <- {Rule[x, 1.5], Rule[y, -1.5]}Complex[-6.333545379831845, 3.3543957304704977] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 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) |
EllipticF[ArcCos[Sqrt[0/z]],(z-z - 1)/(z-0)]/Sqrt[z-0] == EllipticF[ArcCos[Sqrt[0/1]],(1-1 - z)/(1-0)]/Sqrt[1-0]- I*EllipticF[ArcCos[Sqrt[0/1]],(1-z)/(1-0)]/Sqrt[1-0] |
Failure | Failure | Failed [7 / 7] 7/7]: [[3.197606220-2.012137137*I <- {z = 1/2*3^(1/2)+1/2*I}1.024722154-2.538160454*I <- {z = -1/2+1/2*I*3^(1/2)} |
Failed [7 / 7]
{Complex[0.447882135735306, 1.6422203572966838] <- {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.9112982419758283, 0.8007121244739206] <- {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 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) |
EllipticF[ArcCos[Sqrt[0/z]],(z-z - 1)/(z-0)]/Sqrt[z-0] == EllipticF[ArcCos[Sqrt[0/1]],(1-1 - z)/(1-0)]/Sqrt[1-0]+ I*EllipticF[ArcCos[Sqrt[0/1]],(1-z)/(1-0)]/Sqrt[1-0] |
Failure | Failure | Failed [7 / 7] 7/7]: [[3.609429842+1.115973839*I <- {z = 1/2*3^(1/2)+1/2*I}2.710472508+.381644808*I <- {z = -1/2+1/2*I*3^(1/2)} |
Failed [7 / 7]
{Complex[0.0036174998504115152, -2.054982714938571] <- {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.9086726238549093, -2.7316000638683375] <- {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.21.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRG@{0}{z-1}{z} = 2\CarlsonsymellintRG@{0}{1-z}{1}+\iunit 2\CarlsonsymellintRG@{0}{z}{1}+(z-1)\CarlsonsymellintRF@{0}{1-z}{1}-\iunit z\CarlsonsymellintRF@{0}{z}{1}} | Error |
2*Sqrt[z-0]*(EllipticE[ArcCos[Sqrt[0/z]],(z-z - 1)/(z-0)]+(Cot[ArcCos[Sqrt[0/z]]])^2*EllipticF[ArcCos[Sqrt[0/z]],(z-z - 1)/(z-0)]+Cot[ArcCos[Sqrt[0/z]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/z]]]^2]) == 2*Sqrt[1-0]*(EllipticE[ArcCos[Sqrt[0/1]],(1-1 - z)/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2*EllipticF[ArcCos[Sqrt[0/1]],(1-1 - z)/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2])+ I*2*Sqrt[1-0]*(EllipticE[ArcCos[Sqrt[0/1]],(1-z)/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2*EllipticF[ArcCos[Sqrt[0/1]],(1-z)/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2])+(z - 1)* EllipticF[ArcCos[Sqrt[0/1]],(1-1 - z)/(1-0)]/Sqrt[1-0]- I*z*EllipticF[ArcCos[Sqrt[0/1]],(1-z)/(1-0)]/Sqrt[1-0] |
Missing Macro Error | Failure | - | Failed [7 / 7]
{Complex[0.23313173408598564, -1.9381268036446178] <- {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.6842698833888152, -2.1985132995849304] <- {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.21.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRG@{0}{z-1}{z} = 2\CarlsonsymellintRG@{0}{1-z}{1}-\iunit 2\CarlsonsymellintRG@{0}{z}{1}+(z-1)\CarlsonsymellintRF@{0}{1-z}{1}+\iunit z\CarlsonsymellintRF@{0}{z}{1}} | Error |
2*Sqrt[z-0]*(EllipticE[ArcCos[Sqrt[0/z]],(z-z - 1)/(z-0)]+(Cot[ArcCos[Sqrt[0/z]]])^2*EllipticF[ArcCos[Sqrt[0/z]],(z-z - 1)/(z-0)]+Cot[ArcCos[Sqrt[0/z]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/z]]]^2]) == 2*Sqrt[1-0]*(EllipticE[ArcCos[Sqrt[0/1]],(1-1 - z)/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2*EllipticF[ArcCos[Sqrt[0/1]],(1-1 - z)/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2])- I*2*Sqrt[1-0]*(EllipticE[ArcCos[Sqrt[0/1]],(1-z)/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2*EllipticF[ArcCos[Sqrt[0/1]],(1-z)/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2])+(z - 1)* EllipticF[ArcCos[Sqrt[0/1]],(1-1 - z)/(1-0)]/Sqrt[1-0]+ I*z*EllipticF[ArcCos[Sqrt[0/1]],(1-z)/(1-0)]/Sqrt[1-0] |
Missing Macro Error | Failure | - | Failed [7 / 7]
{Complex[0.44709928924442033, 1.6621495887309192] <- {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.1273665829731985, 1.9939163092606038] <- {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.21.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\sqrt{rp}/z)\CarlsonsymellintRJ@{0}{y}{z}{p} = {(r-1)}\CarlsonsymellintRF@{0}{y}{z}\CarlsonsymellintRD@{p}{rz}{z}+\CarlsonsymellintRD@{0}{y}{z}\CarlsonsymellintRF@{p}{rz}{z}} | Error |
(Sqrt[r*p]/(x + y*I))* 3*(x + y*I-0)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-0),ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/Sqrt[x + y*I-0] == (r - 1)*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0]*3*(EllipticF[ArcCos[Sqrt[p/x + y*I]],(x + y*I-r*(x + y*I))/(x + y*I-p)]-EllipticE[ArcCos[Sqrt[p/x + y*I]],(x + y*I-r*(x + y*I))/(x + y*I-p)])/((x + y*I-r*(x + y*I))*(x + y*I-p)^(1/2))+ 3*(EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/((x + y*I-y)*(x + y*I-0)^(1/2))*EllipticF[ArcCos[Sqrt[p/x + y*I]],(x + y*I-r*(x + y*I))/(x + y*I-p)]/Sqrt[x + y*I-p] |
Missing Macro Error | Aborted | - | Failed [300 / 300]
{Complex[-0.019107479205769995, -0.26821779662698253] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[r, -1.5], Rule[x, 1.5], Rule[y, -1.5]}Complex[1.626010920193221, 0.604709928225457] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[r, -1.5], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.21.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (x-y)\CarlsonsymellintRD@{y}{z}{x}+(z-y)\CarlsonsymellintRD@{x}{y}{z} = 3\CarlsonsymellintRF@{x}{y}{z}-3\sqrt{y/(xz)}} | Error |
(x - y)* 3*(EllipticF[ArcCos[Sqrt[y/x]],(x-x + y*I)/(x-y)]-EllipticE[ArcCos[Sqrt[y/x]],(x-x + y*I)/(x-y)])/((x-x + y*I)*(x-y)^(1/2))+((x + y*I)- y)* 3*(EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/((x + y*I-y)*(x + y*I-x)^(1/2)) == 3*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x]- 3*Sqrt[y/(x*(x + y*I))] |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Complex[2.01816993619941, -7.647648832317454] <- {Rule[x, 1.5], Rule[y, -1.5]}Complex[1.9029767059950156, 2.211761239496786] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.21.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRD@{y}{z}{x}+\CarlsonsymellintRD@{z}{x}{y}+\CarlsonsymellintRD@{x}{y}{z} = 3(xyz)^{-1/2}} | Error |
3*(EllipticF[ArcCos[Sqrt[y/x]],(x-x + y*I)/(x-y)]-EllipticE[ArcCos[Sqrt[y/x]],(x-x + y*I)/(x-y)])/((x-x + y*I)*(x-y)^(1/2))+ 3*(EllipticF[ArcCos[Sqrt[x + y*I/y]],(y-x)/(y-x + y*I)]-EllipticE[ArcCos[Sqrt[x + y*I/y]],(y-x)/(y-x + y*I)])/((y-x)*(y-x + y*I)^(1/2))+ 3*(EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/((x + y*I-y)*(x + y*I-x)^(1/2)) == 3*(x*y*(x + y*I))^(- 1/ 2) |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Complex[0.061772053426947915, 0.22732915812456822] <- {Rule[x, 1.5], Rule[y, -1.5]}Indeterminate <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.21.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x\CarlsonsymellintRD@{y}{z}{x}+y\CarlsonsymellintRD@{z}{x}{y}+z\CarlsonsymellintRD@{x}{y}{z} = 3\CarlsonsymellintRF@{x}{y}{z}} | Error |
x*3*(EllipticF[ArcCos[Sqrt[y/x]],(x-x + y*I)/(x-y)]-EllipticE[ArcCos[Sqrt[y/x]],(x-x + y*I)/(x-y)])/((x-x + y*I)*(x-y)^(1/2))+ y*3*(EllipticF[ArcCos[Sqrt[x + y*I/y]],(y-x)/(y-x + y*I)]-EllipticE[ArcCos[Sqrt[x + y*I/y]],(y-x)/(y-x + y*I)])/((y-x)*(y-x + y*I)^(1/2))+(x + y*I)* 3*(EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/((x + y*I-y)*(x + y*I-x)^(1/2)) == 3*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] |
Missing Macro Error | Aborted | - | Failed [18 / 18]
{Complex[0.3490343350525606, -4.182689157514275] <- {Rule[x, 1.5], Rule[y, -1.5]}Indeterminate <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.21.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRG@{x}{y}{z} = z\CarlsonsymellintRF@{x}{y}{z}-\tfrac{1}{3}(x-z)(y-z)\CarlsonsymellintRD@{x}{y}{z}+\sqrt{xy/z}} | Error |
2*Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) == (x + y*I)* EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x]-Divide[1,3]*(x -(x + y*I))*(y -(x + y*I))* 3*(EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/((x + y*I-y)*(x + y*I-x)^(1/2))+Sqrt[x*y/(x + y*I)] |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Plus[Complex[-2.045465659795318, -0.2973389532409781], Times[Complex[1.7320508075688772, -1.732050807568877], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, -1.5]}Plus[Complex[-2.0191372830755783, 1.5655011975568338], Times[Complex[1.7320508075688772, 1.732050807568877], Plus[Complex[1.0566228789425183, 0.3443432776585209], Times[Complex[0.3176872874027722, 1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.21.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p-x)\CarlsonsymellintRJ@{x}{y}{z}{p}+(q-x)\CarlsonsymellintRJ@{x}{y}{z}{q} = 3\CarlsonsymellintRF@{x}{y}{z}-3\CarlsonellintRC@{\xi}{\eta}} | Error |
(p - x)* 3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x]+(q - x)* 3*(x + y*I-x)/(x + y*I-q)*(EllipticPi[(x + y*I-q)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] == 3*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x]- 3*1/Sqrt[\[Eta]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Xi])/(\[Eta])] |
Missing Macro Error | Aborted | - | Failed [300 / 300]
{Indeterminate <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[η, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ξ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[5.153237655786464, -3.718995107844719] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[η, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ξ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.21#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p-x)(q-x) = (y-x)(z-x)} | (p - x)*(q - x) = (y - x)*((x + y*I)- x) |
(p - x)*(q - x) == (y - x)*((x + y*I)- x) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.21#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \xi = yz/x} | xi = y*z/ x |
\[Xi] == y*z/ x |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.21#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta = pq/x} | eta = p*q/ x |
\[Eta] == p*q/ x |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.21.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta-\xi = p+q-y-z} | eta - xi = p + q - y -(x + y*I) |
\[Eta]- \[Xi] == p + q - y -(x + y*I) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.21.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p\CarlsonsymellintRJ@{0}{y}{z}{p}+q\CarlsonsymellintRJ@{0}{y}{z}{q} = 3\CarlsonsymellintRF@{0}{y}{z}} | Error |
p*3*(x + y*I-0)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-0),ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/Sqrt[x + y*I-0]+ q*3*(x + y*I-0)/(x + y*I-q)*(EllipticPi[(x + y*I-q)/(x + y*I-0),ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/Sqrt[x + y*I-0] == 3*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Complex[-0.5878632565330948, -3.2355968294614907] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}Complex[-2.320767562800481, 3.5603464097743847] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} |