Formula:KLS:09.08:35

<< Formula:KLS:09.08:34

formula in Jacobi: Special cases

Formula:KLS:09.08:36 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Ultra{\lambda}{n}@{\cos@@{\theta}} =\frac{\pochhammer{\lambda}{n}}{n!} \sum_{k=0}^\infty\frac{\pochhammer{\lambda}{k}\pochhammer{1-\lambda}{k}}{\pochhammer{1-\lambda-n}{k} k!} \frac{\cos@{(n-k+\lambda)\theta+\frac12(k-\lambda)\cpi}}{(2\sin@@{\theta})^{k+\lambda}} }}

Proof

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Symbols List

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 \mathrm{cos}}}  : cosine function : http://dlmf.nist.gov/4.14#E2
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 \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 \mathrm{sin}}}  : sine function : http://dlmf.nist.gov/4.14#E1

Bibliography

Equation in Section 9.8 of KLS.

URL links

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<< Formula:KLS:09.08:34

formula in Jacobi: Special cases

Formula:KLS:09.08:36 >>