Formula:KLS:09.05:18

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formula in Hahn

Formula:KLS:09.05:19 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \omega(x;\alpha,\beta,N)\Hahn{n}@{x}{\alpha}{\beta}{N} {}=\frac{(-1)^n\pochhammer{\beta+1}{n}}{\pochhammer{-N}{n}}\nabla^n\left[\omega(x;\alpha+n,\beta+n,N-n)\right] }}

Substitution(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \omega(x;\alpha,\beta,N)=\binomial{\alpha+x}{x}\binomial{\beta+N-x}{N-x}}}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle Q_{n}}}  : Hahn polynomial : http://dlmf.nist.gov/18.19#T1.t1.r3
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle (a)_n}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \binom{n}{k}}}  : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1

Bibliography

Equation in Section 9.5 of KLS.

URL links

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formula in Hahn

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