Formula:KLS:09.08:31

<< Formula:KLS:09.08:30

formula in Jacobi: Special cases

Formula:KLS:09.08:32 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \sum_{n=0}^\infty\frac{\lambda+n}\lambda \frac{n!}{\pochhammer{2\lambda}{n}} r^n \Ultra{\lambda}{n}@{x} \Ultra{\lambda}{n}@{y} =\frac{1-r^2}{(1-2rxy+r^2)^{\lambda+1}} \HyperpFq{2}{1}@@{\frac12(\lambda+1),\frac12(\lambda+2)}{\lambda+\frac12}{\frac{4r^2(1-x^2)(1-y^2)}{(1-2rxy+r^2)^2}} (r\in(-1,1),\;x,y\in[-1,1]) }}

Proof

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Symbols List

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 C^{\mu}_{n}}}  : ultraspherical/Gegenbauer polynomial : http://dlmf.nist.gov/18.3#T1.t1.r5
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 \in}}  : element of : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r9

Bibliography

Equation in Section 9.8 of KLS.

URL links

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<< Formula:KLS:09.08:30

formula in Jacobi: Special cases

Formula:KLS:09.08:32 >>