Heun Functions - 31.15 Stieltjes Polynomials
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 31.15.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}+\left(\sum_{j=1}^{N}\frac{\gamma_{j}}{z-a_{j}}\right)\deriv{w}{z}+\frac{\Phi(z)}{\prod_{j=1}^{N}(z-a_{j})}w = 0}
\deriv[2]{w}{z}+\left(\sum_{j=1}^{N}\frac{\gamma_{j}}{z-a_{j}}\right)\deriv{w}{z}+\frac{\Phi(z)}{\prod_{j=1}^{N}(z-a_{j})}w = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(w, [z$(2)])+(sum((gamma[j])/(z - a[j]), j = 1..N))*diff(w, z)+(Phi(z))/(product(z - a[j], j = 1..N))*w = 0
|
D[w, {z, 2}]+(Sum[Divide[Subscript[\[Gamma], j],z - Subscript[a, j]], {j, 1, N}, GenerateConditions->None])*D[w, z]+Divide[\[CapitalPhi][z],Product[z - Subscript[a, j], {j, 1, N}, GenerateConditions->None]]*w == 0
|
Failure | Failure | Error | Failed [300 / 300]
Result: Times[Complex[0.0, 1.0], Power[NProduct[0
Test Values: {j, 1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]}, Rule[GenerateConditions, None]], -1]], {Rule[N, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Φ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[γ, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Times[Complex[0.0, 1.0], Power[NProduct[0
Test Values: {j, 1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]}, Rule[GenerateConditions, None]], -1]], {Rule[N, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Φ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[γ, j], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 31.15#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{j} > 0}
\gamma_{j} > 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | gamma[j] > 0 |
Subscript[\[Gamma], j] > 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 31.15.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{j} = \gamma_{j}\sum_{k=1}^{n}\frac{1}{z_{k}-a_{j}}}
q_{j} = \gamma_{j}\sum_{k=1}^{n}\frac{1}{z_{k}-a_{j}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle j = 1} | q[j] = gamma[j]*sum((1)/(z[k]- a[j]), k = 1..n) |
Subscript[q, j] == Subscript[\[Gamma], j]*Sum[Divide[1,Subscript[z, k]- Subscript[a, j]], {k, 1, n}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |