Formula:KLS:09.08:16

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formula in Jacobi

Formula:KLS:09.08:17 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \HyperpFq{2}{1}@@{\gamma,\alpha+\beta+1-\gamma}{\alpha+1}{\frac{1-R-t}{2}}\ \HyperpFq{2}{1}@@{\gamma,\alpha+\beta+1-\gamma}{\beta+1}{\frac{1-R+t}{2}} {}=\sum_{n=0}^{\infty} \frac{\pochhammer{\gamma}{n}\pochhammer{\alpha+\beta+1-\gamma}{n}}{\pochhammer{\alpha+1}{n}\pochhammer{\beta+1}{n}}\Jacobi{\alpha}{\beta}{n}@{x}t^n }}

Substitution(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle R=\sqrt{1-2xt+t^2}}}

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

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 \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

Bibliography

Equation in Section 9.8 of KLS.

URL links

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<< Formula:KLS:09.08:15

formula in Jacobi

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