Painlevé Transcendents - 32.7 Bäcklund Transformations
Jump to navigation
Jump to search
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 32.7.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle W(\zeta;\tfrac{1}{2}\varepsilon) = \frac{2^{-1/3}\varepsilon}{w(z;0)}\deriv{}{z}w(z;0)}
W(\zeta;\tfrac{1}{2}\varepsilon) = \frac{2^{-1/3}\varepsilon}{w(z;0)}\deriv{}{z}w(z;0) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | W(zeta ;(1)/(2)*varepsilon) = ((2)^(- 1/3)* varepsilon)/(w(z ; 0))*diff(w(z ; 0), z)
|
W[\[Zeta];Divide[1,2]*\[CurlyEpsilon]] == Divide[(2)^(- 1/3)* \[CurlyEpsilon],w[z ; 0]]*D[w[z ; 0], z]
|
Translation Error | Translation Error | - | - |
| 32.7.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w^{2}(z;0) = 2^{-1/3}\left(W^{2}(\zeta;\tfrac{1}{2}\varepsilon)-\varepsilon\deriv{}{\zeta}W(\zeta;\tfrac{1}{2}\varepsilon)+\tfrac{1}{2}\zeta\right)}
w^{2}(z;0) = 2^{-1/3}\left(W^{2}(\zeta;\tfrac{1}{2}\varepsilon)-\varepsilon\deriv{}{\zeta}W(\zeta;\tfrac{1}{2}\varepsilon)+\tfrac{1}{2}\zeta\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (w(z ; 0))^(2) = (2)^(- 1/3)*((W(zeta ;(1)/(2)*varepsilon))^(2)- varepsilon*diff(W(zeta ;(1)/(2)*varepsilon)+(1)/(2)*zeta, zeta))
|
(w[z ; 0])^(2) == (2)^(- 1/3)*((W[\[Zeta];Divide[1,2]*\[CurlyEpsilon]])^(2)- \[CurlyEpsilon]*D[W[\[Zeta];Divide[1,2]*\[CurlyEpsilon]]+Divide[1,2]*\[Zeta], \[Zeta]])
|
Translation Error | Translation Error | - | - |
| 32.7.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\alpha+\tfrac{1}{2}}{w_{\alpha+1}+w_{\alpha}}+\frac{\alpha-\tfrac{1}{2}}{w_{\alpha}+w_{\alpha-1}}+2w_{\alpha}^{2}+z = 0}
\frac{\alpha+\tfrac{1}{2}}{w_{\alpha+1}+w_{\alpha}}+\frac{\alpha-\tfrac{1}{2}}{w_{\alpha}+w_{\alpha-1}}+2w_{\alpha}^{2}+z = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (alpha +(1)/(2))/(w[alpha + 1]+ w[alpha])+(alpha -(1)/(2))/(w[alpha]+ w[alpha - 1])+ 2*(w[alpha])^(2)+ z = 0 |
Divide[\[Alpha]+Divide[1,2],Subscript[w, \[Alpha]+ 1]+ Subscript[w, \[Alpha]]]+Divide[\[Alpha]-Divide[1,2],Subscript[w, \[Alpha]]+ Subscript[w, \[Alpha]- 1]]+ 2*(Subscript[w, \[Alpha]])^(2)+ z == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha_{1},\beta_{1},\gamma_{1},\delta_{1}) = (-\alpha_{0},-\beta_{0},\gamma_{0},\delta_{0})}
(\alpha_{1},\beta_{1},\gamma_{1},\delta_{1}) = (-\alpha_{0},-\beta_{0},\gamma_{0},\delta_{0}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (alpha[1], beta[1], gamma[1], delta[1]) = (- alpha[0], - beta[0], gamma[0], delta[0]) |
(Subscript[\[Alpha], 1], Subscript[\[Beta], 1], Subscript[\[Gamma], 1], Subscript[\[Delta], 1]) == (- Subscript[\[Alpha], 0], - Subscript[\[Beta], 0], Subscript[\[Gamma], 0], Subscript[\[Delta], 0]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha_{2},\beta_{2},\gamma_{2},\delta_{2}) = (-\beta_{0},-\alpha_{0},-\delta_{0},-\gamma_{0})}
(\alpha_{2},\beta_{2},\gamma_{2},\delta_{2}) = (-\beta_{0},-\alpha_{0},-\delta_{0},-\gamma_{0}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (alpha[2], beta[2], gamma[2], delta[2]) = (- beta[0], - alpha[0], - delta[0], - gamma[0]) |
(Subscript[\[Alpha], 2], Subscript[\[Beta], 2], Subscript[\[Gamma], 2], Subscript[\[Delta], 2]) == (- Subscript[\[Beta], 0], - Subscript[\[Alpha], 0], - Subscript[\[Delta], 0], - Subscript[\[Gamma], 0]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{1} = \alpha_{3}}
\alpha_{1} = \alpha_{3} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | alpha[1] = alpha[3] |
Subscript[\[Alpha], 1] == Subscript[\[Alpha], 3] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{2} = \alpha_{4}}
\alpha_{2} = \alpha_{4} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | alpha[2] = alpha[4] |
Subscript[\[Alpha], 2] == Subscript[\[Alpha], 4] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{1} = \beta_{2}}
\beta_{1} = \beta_{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | beta[1] = beta[2] |
Subscript[\[Beta], 1] == Subscript[\[Beta], 2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{3} = \beta_{4}}
\beta_{3} = \beta_{4} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | beta[3] = beta[4] |
Subscript[\[Beta], 3] == Subscript[\[Beta], 4] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{5} = \beta_{0}+2}
\beta_{5} = \beta_{0}+2 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | beta[5] = beta[0]+ 2 |
Subscript[\[Beta], 5] == Subscript[\[Beta], 0]+ 2 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{6} = \beta_{0}-2}
\beta_{6} = \beta_{0}-2 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | beta[6] = beta[0]- 2 |
Subscript[\[Beta], 6] == Subscript[\[Beta], 0]- 2 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z;a,b,0,0) = W^{2}(\zeta;0,0,a,b)}
w(z;a,b,0,0) = W^{2}(\zeta;0,0,a,b) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | w(z ; a , b , 0 , 0) = (W(zeta ; 0 , 0 , a , b))^(2) |
w[z ; a , b , 0 , 0] == (W[\[Zeta]; 0 , 0 , a , b])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \tfrac{1}{2}\zeta^{2}}
z = \tfrac{1}{2}\zeta^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | z = (1)/(2)*(zeta)^(2) |
z == Divide[1,2]*\[Zeta]^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{1}^{+} = \tfrac{1}{4}\left(2-2\alpha_{0}+ 3\sqrt{-2\beta_{0}}\right)}
\alpha_{1}^{+} = \tfrac{1}{4}\left(2-2\alpha_{0}+ 3\sqrt{-2\beta_{0}}\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (alpha[1])^(+) = (1)/(4)*(2 - 2*alpha[0]+ 3*sqrt(- 2*beta[0])) |
(Subscript[\[Alpha], 1])^(+) == Divide[1,4]*(2 - 2*Subscript[\[Alpha], 0]+ 3*Sqrt[- 2*Subscript[\[Beta], 0]]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{1}^{+} = -\tfrac{1}{2}\left(1+\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2}}
\beta_{1}^{+} = -\tfrac{1}{2}\left(1+\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (beta[1])^(+) = -(1)/(2)*(1 + alpha[0]+(1)/(2)*sqrt(- 2*beta[0]))^(2) |
(Subscript[\[Beta], 1])^(+) == -Divide[1,2]*(1 + Subscript[\[Alpha], 0]+Divide[1,2]*Sqrt[- 2*Subscript[\[Beta], 0]])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{2}^{+} = -\tfrac{1}{4}\left(2+2\alpha_{0}+ 3\sqrt{-2\beta_{0}}\right)}
\alpha_{2}^{+} = -\tfrac{1}{4}\left(2+2\alpha_{0}+ 3\sqrt{-2\beta_{0}}\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (alpha[2])^(+) = -(1)/(4)*(2 + 2*alpha[0]+ 3*sqrt(- 2*beta[0])) |
(Subscript[\[Alpha], 2])^(+) == -Divide[1,4]*(2 + 2*Subscript[\[Alpha], 0]+ 3*Sqrt[- 2*Subscript[\[Beta], 0]]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{2}^{+} = -\tfrac{1}{2}\left(1-\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2}}
\beta_{2}^{+} = -\tfrac{1}{2}\left(1-\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (beta[2])^(+) = -(1)/(2)*(1 - alpha[0]+(1)/(2)*sqrt(- 2*beta[0]))^(2) |
(Subscript[\[Beta], 2])^(+) == -Divide[1,2]*(1 - Subscript[\[Alpha], 0]+Divide[1,2]*Sqrt[- 2*Subscript[\[Beta], 0]])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{3}^{+} = \tfrac{3}{2}-\tfrac{1}{2}\alpha_{0}-\tfrac{3}{4}\sqrt{-2\beta_{0}}}
\alpha_{3}^{+} = \tfrac{3}{2}-\tfrac{1}{2}\alpha_{0}-\tfrac{3}{4}\sqrt{-2\beta_{0}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (alpha[3])^(+) = (3)/(2)-(1)/(2)*alpha[0]-(3)/(4)*sqrt(- 2*beta[0]) |
(Subscript[\[Alpha], 3])^(+) == Divide[3,2]-Divide[1,2]*Subscript[\[Alpha], 0]-Divide[3,4]*Sqrt[- 2*Subscript[\[Beta], 0]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{3}^{+} = -\tfrac{1}{2}\left(1-\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2}}
\beta_{3}^{+} = -\tfrac{1}{2}\left(1-\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (beta[3])^(+) = -(1)/(2)*(1 - alpha[0]+(1)/(2)*sqrt(- 2*beta[0]))^(2) |
(Subscript[\[Beta], 3])^(+) == -Divide[1,2]*(1 - Subscript[\[Alpha], 0]+Divide[1,2]*Sqrt[- 2*Subscript[\[Beta], 0]])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{4}^{+} = -\tfrac{3}{2}-\tfrac{1}{2}\alpha_{0}-\tfrac{3}{4}\sqrt{-2\beta_{0}}}
\alpha_{4}^{+} = -\tfrac{3}{2}-\tfrac{1}{2}\alpha_{0}-\tfrac{3}{4}\sqrt{-2\beta_{0}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (alpha[4])^(+) = -(3)/(2)-(1)/(2)*alpha[0]-(3)/(4)*sqrt(- 2*beta[0]) |
(Subscript[\[Alpha], 4])^(+) == -Divide[3,2]-Divide[1,2]*Subscript[\[Alpha], 0]-Divide[3,4]*Sqrt[- 2*Subscript[\[Beta], 0]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{4}^{+} = -\tfrac{1}{2}\left(-1-\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2}}
\beta_{4}^{+} = -\tfrac{1}{2}\left(-1-\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (beta[4])^(+) = -(1)/(2)*(- 1 - alpha[0]+(1)/(2)*sqrt(- 2*beta[0]))^(2) |
(Subscript[\[Beta], 4])^(+) == -Divide[1,2]*(- 1 - Subscript[\[Alpha], 0]+Divide[1,2]*Sqrt[- 2*Subscript[\[Beta], 0]])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1} = -z_{0}}
z_{1} = -z_{0} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | z[1] = - z[0] |
Subscript[z, 1] == - Subscript[z, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{2} = z_{0}}
z_{2} = z_{0} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | z[2] = z[0] |
Subscript[z, 2] == Subscript[z, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha_{1},\beta_{1},\gamma_{1},\delta_{1}) = (\alpha_{0},\beta_{0},-\gamma_{0},\delta_{0})}
(\alpha_{1},\beta_{1},\gamma_{1},\delta_{1}) = (\alpha_{0},\beta_{0},-\gamma_{0},\delta_{0}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (alpha[1], beta[1], gamma[1], delta[1]) = (alpha[0], beta[0], - gamma[0], delta[0]) |
(Subscript[\[Alpha], 1], Subscript[\[Beta], 1], Subscript[\[Gamma], 1], Subscript[\[Delta], 1]) == (Subscript[\[Alpha], 0], Subscript[\[Beta], 0], - Subscript[\[Gamma], 0], Subscript[\[Delta], 0]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha_{2},\beta_{2},\gamma_{2},\delta_{2}) = (-\beta_{0},-\alpha_{0},-\gamma_{0},\delta_{0})}
(\alpha_{2},\beta_{2},\gamma_{2},\delta_{2}) = (-\beta_{0},-\alpha_{0},-\gamma_{0},\delta_{0}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (alpha[2], beta[2], gamma[2], delta[2]) = (- beta[0], - alpha[0], - gamma[0], delta[0]) |
(Subscript[\[Alpha], 2], Subscript[\[Beta], 2], Subscript[\[Gamma], 2], Subscript[\[Delta], 2]) == (- Subscript[\[Beta], 0], - Subscript[\[Alpha], 0], - Subscript[\[Gamma], 0], Subscript[\[Delta], 0]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{1} = \tfrac{1}{8}\left(\gamma_{0}+\varepsilon_{1}\left(1-\varepsilon_{3}\sqrt{-2\beta_{0}}-\varepsilon_{2}\sqrt{2\alpha_{0}}\right)\right)^{2}}
\alpha_{1} = \tfrac{1}{8}\left(\gamma_{0}+\varepsilon_{1}\left(1-\varepsilon_{3}\sqrt{-2\beta_{0}}-\varepsilon_{2}\sqrt{2\alpha_{0}}\right)\right)^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | alpha[1] = (1)/(8)*(gamma[0]+ varepsilon[1]*(1 - varepsilon[3]*sqrt(- 2*beta[0])- varepsilon[2]*sqrt(2*alpha[0])))^(2) |
Subscript[\[Alpha], 1] == Divide[1,8]*(Subscript[\[Gamma], 0]+ Subscript[\[CurlyEpsilon], 1]*(1 - Subscript[\[CurlyEpsilon], 3]*Sqrt[- 2*Subscript[\[Beta], 0]]- Subscript[\[CurlyEpsilon], 2]*Sqrt[2*Subscript[\[Alpha], 0]]))^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{1} = -\tfrac{1}{8}\left(\gamma_{0}-\varepsilon_{1}\left(1-\varepsilon_{3}\sqrt{-2\beta_{0}}-\varepsilon_{2}\sqrt{2\alpha_{0}}\right)\right)^{2}}
\beta_{1} = -\tfrac{1}{8}\left(\gamma_{0}-\varepsilon_{1}\left(1-\varepsilon_{3}\sqrt{-2\beta_{0}}-\varepsilon_{2}\sqrt{2\alpha_{0}}\right)\right)^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | beta[1] = -(1)/(8)*(gamma[0]- varepsilon[1]*(1 - varepsilon[3]*sqrt(- 2*beta[0])- varepsilon[2]*sqrt(2*alpha[0])))^(2) |
Subscript[\[Beta], 1] == -Divide[1,8]*(Subscript[\[Gamma], 0]- Subscript[\[CurlyEpsilon], 1]*(1 - Subscript[\[CurlyEpsilon], 3]*Sqrt[- 2*Subscript[\[Beta], 0]]- Subscript[\[CurlyEpsilon], 2]*Sqrt[2*Subscript[\[Alpha], 0]]))^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{1} = \varepsilon_{1}\left(\varepsilon_{3}\sqrt{-2\beta_{0}}-\varepsilon_{2}\sqrt{2\alpha_{0}}\right)}
\gamma_{1} = \varepsilon_{1}\left(\varepsilon_{3}\sqrt{-2\beta_{0}}-\varepsilon_{2}\sqrt{2\alpha_{0}}\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | gamma[1] = varepsilon[1]*(varepsilon[3]*sqrt(- 2*beta[0])- varepsilon[2]*sqrt(2*alpha[0])) |
Subscript[\[Gamma], 1] == Subscript[\[CurlyEpsilon], 1]*(Subscript[\[CurlyEpsilon], 3]*Sqrt[- 2*Subscript[\[Beta], 0]]- Subscript[\[CurlyEpsilon], 2]*Sqrt[2*Subscript[\[Alpha], 0]]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle W(\zeta;\alpha_{0},\beta_{0},\gamma_{0},\delta_{0}) = \frac{v-1}{v+1}}
W(\zeta;\alpha_{0},\beta_{0},\gamma_{0},\delta_{0}) = \frac{v-1}{v+1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | W(zeta ; alpha[0], beta[0], gamma[0], delta[0]) = (v - 1)/(v + 1) |
W[\[Zeta]; Subscript[\[Alpha], 0], Subscript[\[Beta], 0], Subscript[\[Gamma], 0], Subscript[\[Delta], 0]] == Divide[v - 1,v + 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \sqrt{2\zeta}}
z = \sqrt{2\zeta} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | z = sqrt(2*zeta) |
z == Sqrt[2*\[Zeta]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha_{0},\beta_{0},\gamma_{0},\delta_{0}) = {\left((\beta-\varepsilon\alpha+2)^{2}/32,-(\beta+\varepsilon\alpha-2)^{2}/32,-\varepsilon,0\right)}}
(\alpha_{0},\beta_{0},\gamma_{0},\delta_{0}) = {\left((\beta-\varepsilon\alpha+2)^{2}/32,-(\beta+\varepsilon\alpha-2)^{2}/32,-\varepsilon,0\right)} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (alpha[0], beta[0], gamma[0], delta[0]) = ((beta - varepsilon*alpha + 2)^(2)/32 , -(beta + varepsilon*alpha - 2)^(2)/32 , - varepsilon , 0) |
(Subscript[\[Alpha], 0], Subscript[\[Beta], 0], Subscript[\[Gamma], 0], Subscript[\[Delta], 0]) == ((\[Beta]- \[CurlyEpsilon]*\[Alpha]+ 2)^(2)/32 , -(\[Beta]+ \[CurlyEpsilon]*\[Alpha]- 2)^(2)/32 , - \[CurlyEpsilon], 0) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1} = 1/z_{0}}
z_{1} = 1/z_{0} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | z[1] = 1/z[0] |
Subscript[z, 1] == 1/Subscript[z, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{2} = 1-z_{0}}
z_{2} = 1-z_{0} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | z[2] = 1 - z[0] |
Subscript[z, 2] == 1 - Subscript[z, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E35 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{3} = 1/z_{0}}
z_{3} = 1/z_{0} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | z[3] = 1/z[0] |
Subscript[z, 3] == 1/Subscript[z, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha_{1},\beta_{1},\gamma_{1},\delta_{1}) = (\alpha_{0},\beta_{0},-\delta_{0}+\tfrac{1}{2},-\gamma_{0}+\tfrac{1}{2})}
(\alpha_{1},\beta_{1},\gamma_{1},\delta_{1}) = (\alpha_{0},\beta_{0},-\delta_{0}+\tfrac{1}{2},-\gamma_{0}+\tfrac{1}{2}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (alpha[1], beta[1], gamma[1], delta[1]) = (alpha[0], beta[0], - delta[0]+(1)/(2), - gamma[0]+(1)/(2)) |
(Subscript[\[Alpha], 1], Subscript[\[Beta], 1], Subscript[\[Gamma], 1], Subscript[\[Delta], 1]) == (Subscript[\[Alpha], 0], Subscript[\[Beta], 0], - Subscript[\[Delta], 0]+Divide[1,2], - Subscript[\[Gamma], 0]+Divide[1,2]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha_{2},\beta_{2},\gamma_{2},\delta_{2}) = (\alpha_{0},-\gamma_{0},-\beta_{0},\delta_{0})}
(\alpha_{2},\beta_{2},\gamma_{2},\delta_{2}) = (\alpha_{0},-\gamma_{0},-\beta_{0},\delta_{0}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (alpha[2], beta[2], gamma[2], delta[2]) = (alpha[0], - gamma[0], - beta[0], delta[0]) |
(Subscript[\[Alpha], 2], Subscript[\[Beta], 2], Subscript[\[Gamma], 2], Subscript[\[Delta], 2]) == (Subscript[\[Alpha], 0], - Subscript[\[Gamma], 0], - Subscript[\[Beta], 0], Subscript[\[Delta], 0]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E38 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha_{3},\beta_{3},\gamma_{3},\delta_{3}) = (-\beta_{0},-\alpha_{0},\gamma_{0},\delta_{0})}
(\alpha_{3},\beta_{3},\gamma_{3},\delta_{3}) = (-\beta_{0},-\alpha_{0},\gamma_{0},\delta_{0}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (alpha[3], beta[3], gamma[3], delta[3]) = (- beta[0], - alpha[0], gamma[0], delta[0]) |
(Subscript[\[Alpha], 3], Subscript[\[Beta], 3], Subscript[\[Gamma], 3], Subscript[\[Delta], 3]) == (- Subscript[\[Beta], 0], - Subscript[\[Alpha], 0], Subscript[\[Gamma], 0], Subscript[\[Delta], 0]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha,\beta,\gamma,\delta) = \left(\tfrac{1}{2}(\theta_{\infty}-1)^{2},-\tfrac{1}{2}\theta_{0}^{2},\tfrac{1}{2}\theta_{1}^{2},\tfrac{1}{2}(1-\theta_{2}^{2})\right)}
(\alpha,\beta,\gamma,\delta) = \left(\tfrac{1}{2}(\theta_{\infty}-1)^{2},-\tfrac{1}{2}\theta_{0}^{2},\tfrac{1}{2}\theta_{1}^{2},\tfrac{1}{2}(1-\theta_{2}^{2})\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (alpha , beta , gamma , delta) = ((1)/(2)*(theta[infinity]- 1)^(2), -(1)/(2)*(theta[0])^(2),(1)/(2)*(theta[1])^(2),(1)/(2)*(1 - (theta[2])^(2))) |
(\[Alpha], \[Beta], \[Gamma], \[Delta]) == (Divide[1,2]*(Subscript[\[Theta], Infinity]- 1)^(2), -Divide[1,2]*(Subscript[\[Theta], 0])^(2),Divide[1,2]*(Subscript[\[Theta], 1])^(2),Divide[1,2]*(1 - (Subscript[\[Theta], 2])^(2))) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E43 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (A,B,C,D) = \left(\tfrac{1}{2}(\Theta_{\infty}-1)^{2},-\tfrac{1}{2}\Theta_{0}^{2},\tfrac{1}{2}\Theta_{1}^{2},\tfrac{1}{2}(1-\Theta_{2}^{2})\right)}
(A,B,C,D) = \left(\tfrac{1}{2}(\Theta_{\infty}-1)^{2},-\tfrac{1}{2}\Theta_{0}^{2},\tfrac{1}{2}\Theta_{1}^{2},\tfrac{1}{2}(1-\Theta_{2}^{2})\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (A , B , C , D) = ((1)/(2)*(Theta[infinity]- 1)^(2), -(1)/(2)*(Theta[0])^(2),(1)/(2)*(Theta[1])^(2),(1)/(2)*(1 - (Theta[2])^(2))) |
(A , B , C , D) == (Divide[1,2]*(Subscript[\[CapitalTheta], Infinity]- 1)^(2), -Divide[1,2]*(Subscript[\[CapitalTheta], 0])^(2),Divide[1,2]*(Subscript[\[CapitalTheta], 1])^(2),Divide[1,2]*(1 - (Subscript[\[CapitalTheta], 2])^(2))) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E44 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \theta_{j} = \Theta_{j}+\tfrac{1}{2}\sigma}
\theta_{j} = \Theta_{j}+\tfrac{1}{2}\sigma |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | theta[j] = Theta[j]+(1)/(2)*sigma |
Subscript[\[Theta], j] == Subscript[\[CapitalTheta], j]+Divide[1,2]*\[Sigma] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E45 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sigma = \theta_{0}+\theta_{1}+\theta_{2}+\theta_{\infty}-1}
\sigma = \theta_{0}+\theta_{1}+\theta_{2}+\theta_{\infty}-1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sigma = theta[0]+ theta[1]+ theta[2]+ theta[infinity]- 1 |
\[Sigma] == Subscript[\[Theta], 0]+ Subscript[\[Theta], 1]+ Subscript[\[Theta], 2]+ Subscript[\[Theta], Infinity]- 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{1}(\zeta_{1}) = \frac{(1-w)(w-z)}{(1+\sqrt{z})^{2}w}}
u_{1}(\zeta_{1}) = \frac{(1-w)(w-z)}{(1+\sqrt{z})^{2}w} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | u[1](zeta[1]) = ((1 - w)*(w - z))/((1 +sqrt(z))^(2)* w) |
Subscript[u, 1][Subscript[\[Zeta], 1]] == Divide[(1 - w)*(w - z),(1 +Sqrt[z])^(2)* w] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta_{1} = \left(\frac{1-\sqrt{z}}{1+\sqrt{z}}\right)^{2}}
\zeta_{1} = \left(\frac{1-\sqrt{z}}{1+\sqrt{z}}\right)^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | zeta[1] = ((1 -sqrt(z))/(1 +sqrt(z)))^(2) |
Subscript[\[Zeta], 1] == (Divide[1 -Sqrt[z],1 +Sqrt[z]])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{2}(\zeta_{2}) = \frac{(w^{2}-z)^{2}}{4w(w-1)(w-z)}}
u_{2}(\zeta_{2}) = \frac{(w^{2}-z)^{2}}{4w(w-1)(w-z)} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | u[2](zeta[2]) = (((w)^(2)- z)^(2))/(4*w*(w - 1)*(w - z)) |
Subscript[u, 2][Subscript[\[Zeta], 2]] == Divide[((w)^(2)- z)^(2),4*w*(w - 1)*(w - z)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta_{2} = z}
\zeta_{2} = z |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | zeta[2] = z |
Subscript[\[Zeta], 2] == z |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E49 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{3}(\zeta_{3}) = \left(\frac{1-z^{1/4}}{1+z^{1/4}}\right)^{2}\left(\frac{\sqrt{w}+z^{1/4}}{\sqrt{w}-z^{1/4}}\right)^{2}}
u_{3}(\zeta_{3}) = \left(\frac{1-z^{1/4}}{1+z^{1/4}}\right)^{2}\left(\frac{\sqrt{w}+z^{1/4}}{\sqrt{w}-z^{1/4}}\right)^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | u[3](zeta[3]) = ((1 - (z)^(1/4))/(1 + (z)^(1/4)))^(2)*((sqrt(w)+ (z)^(1/4))/(sqrt(w)- (z)^(1/4)))^(2) |
Subscript[u, 3][Subscript[\[Zeta], 3]] == (Divide[1 - (z)^(1/4),1 + (z)^(1/4)])^(2)*(Divide[Sqrt[w]+ (z)^(1/4),Sqrt[w]- (z)^(1/4)])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E50 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta_{3} = \left(\frac{1-z^{1/4}}{1+z^{1/4}}\right)^{4}}
\zeta_{3} = \left(\frac{1-z^{1/4}}{1+z^{1/4}}\right)^{4} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | zeta[3] = ((1 - (z)^(1/4))/(1 + (z)^(1/4)))^(4) |
Subscript[\[Zeta], 3] == (Divide[1 - (z)^(1/4),1 + (z)^(1/4)])^(4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |