Painlevé Transcendents - 32.3 Graphics
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 32.3.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{u}{x} = 3u^{5}+2xu^{3}+\left(\tfrac{1}{4}x^{2}-\nu-\tfrac{1}{2}\right)u}
\deriv[2]{u}{x} = 3u^{5}+2xu^{3}+\left(\tfrac{1}{4}x^{2}-\nu-\tfrac{1}{2}\right)u |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(u, [x$(2)]) = 3*(u)^(5)+ 2*x*(u)^(3)+((1)/(4)*(x)^(2)- nu -(1)/(2))*u
|
D[u, {x, 2}] == 3*(u)^(5)+ 2*x*(u)^(3)+(Divide[1,4]*(x)^(2)- \[Nu]-Divide[1,2])*u
|
Failure | Failure | Failed [300 / 300] Result: 3.043949625-3.665224602*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, x = 3/2}
Result: 3.476962328-1.415224600*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, x = 1/2}
... skip entries to safe data |
Failed [300 / 300]
Result: Complex[3.043949623616789, -3.6652245962155616]
Test Values: {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[1.67792421983235, -4.031249999999999]
Test Values: {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 32.3.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(x) = 2\sqrt{2}u_{k}^{2}(\sqrt{2}x,\nu)}
w(x) = 2\sqrt{2}u_{k}^{2}(\sqrt{2}x,\nu) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | w(x) = 2*sqrt(2)*(u[k])^(2)(sqrt(2)*x , nu) |
w[x] == 2*Sqrt[2]*(Subscript[u, k])^(2)[Sqrt[2]*x , \[Nu]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.3.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u^{2} = -\tfrac{1}{3}x+\tfrac{1}{6}\sqrt{x^{2}+12\nu+6}}
u^{2} = -\tfrac{1}{3}x+\tfrac{1}{6}\sqrt{x^{2}+12\nu+6} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (u)^(2) = -(1)/(3)*x +(1)/(6)*sqrt((x)^(2)+ 12*nu + 6) |
(u)^(2) == -Divide[1,3]*x +Divide[1,6]*Sqrt[(x)^(2)+ 12*\[Nu]+ 6] |
Skipped - no semantic math | Skipped - no semantic math | - | - |