Orthogonal Polynomials - 18.20 Hahn Class: Explicit Representations
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 18.20.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CharlierpolyC{n}@{x}{a} = \genhyperF{2}{0}@@{-n,-x}{-}{-a^{-1}}}
\CharlierpolyC{n}@{x}{a} = \genhyperF{2}{0}@@{-n,-x}{-}{-a^{-1}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
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HypergeometricPFQ[{-(n), -(x)}, {}, -Divide[1,a]] == HypergeometricPFQ[{- n , - x}, {-}, - (a)^(- 1)]
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Missing Macro Error | Missing Macro Error | - | - |
| 18.20.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \contHahnpolyp{n}@{x}{a}{b}{\conj{a}}{\conj{b}} = \frac{\iunit^{n}\Pochhammersym{a+\conj{a}}{n}\Pochhammersym{a+\conj{b}}{n}}{n!}\*\genhyperF{3}{2}@@{-n,n+2\realpart@{a+b}-1,a+\iunit x}{a+\conj{a},a+\conj{b}}{1}}
\contHahnpolyp{n}@{x}{a}{b}{\conj{a}}{\conj{b}} = \frac{\iunit^{n}\Pochhammersym{a+\conj{a}}{n}\Pochhammersym{a+\conj{b}}{n}}{n!}\*\genhyperF{3}{2}@@{-n,n+2\realpart@{a+b}-1,a+\iunit x}{a+\conj{a},a+\conj{b}}{1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
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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] == Divide[(I)^(n)* 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]
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Missing Macro Error | Missing Macro Error | - | - |