Orthogonal Polynomials - 18.23 Hahn Class: Generating Functions
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
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| 18.23.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{z}\left(1-\frac{z}{a}\right)^{x} = \sum_{n=0}^{\infty}\frac{\CharlierpolyC{n}@{x}{a}}{n!}z^{n}}
e^{z}\left(1-\frac{z}{a}\right)^{x} = \sum_{n=0}^{\infty}\frac{\CharlierpolyC{n}@{x}{a}}{n!}z^{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
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Exp[x + y*I]*(1 -Divide[x + y*I,a])^(x) == Sum[Divide[HypergeometricPFQ[{-(n), -(x)}, {}, -Divide[1,a]],(n)!]*(x + y*I)^(n), {n, 0, Infinity}, GenerateConditions->None]
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Missing Macro Error | Missing Macro Error | - | - |
| 18.23.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genhyperF{1}{1}@@{a+\iunit x}{2\realpart@@{a}}{-\iunit z}\genhyperF{1}{1}@@{\conj{b}-\iunit x}{2\realpart@@{b}}{\iunit z} = \sum_{n=0}^{\infty}\frac{\contHahnpolyp{n}@{x}{a}{b}{\conj{a}}{\conj{b}}}{\Pochhammersym{2\realpart@@{a}}{n}\Pochhammersym{2\realpart@@{b}}{n}}z^{n}}
\genhyperF{1}{1}@@{a+\iunit x}{2\realpart@@{a}}{-\iunit z}\genhyperF{1}{1}@@{\conj{b}-\iunit x}{2\realpart@@{b}}{\iunit z} = \sum_{n=0}^{\infty}\frac{\contHahnpolyp{n}@{x}{a}{b}{\conj{a}}{\conj{b}}}{\Pochhammersym{2\realpart@@{a}}{n}\Pochhammersym{2\realpart@@{b}}{n}}z^{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
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HypergeometricPFQ[{a + I*x}, {2*Re[a]}, - I*(x + y*I)]*HypergeometricPFQ[{Conjugate[b]- I*x}, {2*Re[b]}, I*(x + y*I)] == Sum[Divide[I^(n)*Divide[Pochhammer[a + Conjugate[a], n]*Pochhammer[a + Conjugate[b], n], (n)!] * HypergeometricPFQ[{-(n), n + 2*Re[a + b] - 1, a + I*(x)}, {a + Conjugate[a], a + Conjugate[b]}, 1],Pochhammer[2*Re[a], n]*Pochhammer[2*Re[b], n]]*(x + y*I)^(n), {n, 0, Infinity}, GenerateConditions->None]
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Missing Macro Error | Missing Macro Error | - | - |