Heun Functions - 31.14 General Fuchsian Equation
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 31.14.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}+\left(\sum_{j=1}^{N}\frac{q_{j}}{z-a_{j}}\right)w = 0}
\deriv[2]{w}{z}+\left(\sum_{j=1}^{N}\frac{\gamma_{j}}{z-a_{j}}\right)\deriv{w}{z}+\left(\sum_{j=1}^{N}\frac{q_{j}}{z-a_{j}}\right)w = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{j=1}^{N}q_{j} = 0} | diff(w, [z$(2)])+(sum((gamma[j])/(z - a[j]), j = 1..N))*diff(w, z)+(sum((q[j])/(z - a[j]), j = 1..N))*w = 0
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D[w, {z, 2}]+(Sum[Divide[Subscript[\[Gamma], j],z - Subscript[a, j]], {j, 1, N}, GenerateConditions->None])*D[w, z]+(Sum[Divide[Subscript[q, j],z - Subscript[a, j]], {j, 1, N}, GenerateConditions->None])*w == 0
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Skipped - Unable to analyze test case: Null | Skipped - Unable to analyze test case: Null | - | - |
| 31.14#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha+\beta+1 = \sum_{j=1}^{N}\gamma_{j}}
\alpha+\beta+1 = \sum_{j=1}^{N}\gamma_{j} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | alpha + beta + 1 = sum(gamma[j], j = 1..N) |
\[Alpha]+ \[Beta]+ 1 == Sum[Subscript[\[Gamma], j], {j, 1, N}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 31.14#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha\beta = \sum_{j=1}^{N}a_{j}q_{j}}
\alpha\beta = \sum_{j=1}^{N}a_{j}q_{j} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | alpha*beta = sum(a[j]*q[j], j = 1..N) |
\[Alpha]*\[Beta] == Sum[Subscript[a, j]*Subscript[q, j], {j, 1, N}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 31.14.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = \left(\prod_{j=1}^{N}(z-a_{j})^{-\gamma_{j}/2}\right)W(z)}
w(z) = \left(\prod_{j=1}^{N}(z-a_{j})^{-\gamma_{j}/2}\right)W(z) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | w(z) = (product((z - a[j])^(- gamma[j]/2), j = 1..N))*W(z) |
w[z] == (Product[(z - Subscript[a, j])^(- Subscript[\[Gamma], j]/2), {j, 1, N}, GenerateConditions->None])*W[z] |
Skipped - no semantic math | Skipped - no semantic math | - | - |