Formula:KLS:09.08:43

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \normJacobiR{\alpha}{\alpha}{n}@{xy+(1-x^2)^\frac12(1-y^2)^\frac12 t} =\sum_{k=0}^n \frac{(-1)^k\pochhammer{-n}{k} \pochhammer{n+2\alpha+1}{k}}{2^{2k}(\pochhammer{\alpha+1}{k})^2} (1-x^2)^{k/2} \normJacobiR{\alpha+k}{\alpha+k}{n-k}@{x} (1-y^2)^{k/2} \normJacobiR{\alpha+k}{\alpha+k}{n-k}@{y} \omega_k^{(\alpha-\frac12,\alpha-\frac12)} \normJacobiR{\alpha-\frac12}{\alpha-\frac12}{k}@{t} }}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle R^{(\alpha,\beta)}_{n}}}  : normalized Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:normJacobiR
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

Bibliography

Equation in Section 9.8 of KLS.

URL links

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