Formula:KLS:09.04:21

<< Formula:KLS:09.04:20

formula in Continuous Hahn

Formula:KLS:09.04:22 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle (1-t)^{1-a-b-c-d}\,\HyperpFq{3}{2}@@{\frac{1}{2}(a+b+c+d-1),\frac{1}{2}(a+b+c+d),a+\iunit x}{a+c,a+d}{-\frac{4t}{(1-t)^2}} {}=\sum_{n=0}^{\infty} \frac{\pochhammer{a+b+c+d-1}{n}}{\pochhammer{a+c}{n}\pochhammer{a+d}{n}\iunit^n}\ctsHahn{n}@{x}{a}{b}{c}{d}t^n }}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle {{}_{p}F_{q}}}}  : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{i}}}  : imaginary unit : http://dlmf.nist.gov/1.9.i
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Sigma}}  : sum : http://drmf.wmflabs.org/wiki/Definition:sum
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 p_{n}}}  : continuous Hahn polynomial : http://dlmf.nist.gov/18.19#P2.p1

Bibliography

Equation in Section 9.4 of KLS.

URL links

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<< Formula:KLS:09.04:20

formula in Continuous Hahn

Formula:KLS:09.04:22 >>