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formula in Jacobi: Special cases

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \sum_{n=0}^\infty\frac{2n+\alpha+\beta+1}{n+\alpha+\beta+1} \frac{\pochhammer{\alpha+\beta+2}{n} n!}{\pochhammer{\alpha+1}{n}\pochhammer{\beta+1}{n}} r^n \Jacobi{\alpha}{\beta}{n}@{x} \Jacobi{\alpha}{\beta}{n}@{y} =\frac{1-r}{(1+r)^{\alpha+\beta+2}} \AppellFiv@{\frac12(\alpha+\beta+2)}{\frac12(\alpha+\beta+3)}{\alpha+1}{\beta+1}{ \frac{r(1-x)(1-y)}{(1+r)^2}}{\frac{r(1+x)(1+y)}{(1+r)^2}} }}

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 P^{(\alpha,\beta)}_{n}}}  : Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle {F_{4}}}}  : Appell function Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle F_4}}  : http://dlmf.nist.gov/16.13#E4

Bibliography

Equation in Section of KLS.

URL links

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formula in Jacobi: Special cases

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