Formula:KLS:09.09:03

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \frac{1}{2\cpi}\int_{-\infty}^{\infty}(1+x^2)^{-N-1}\expe^{2\nu\atan@@{x}}\pseudoJacobi{m}@{x}{\nu}{N}\pseudoJacobi{n}@{x}{\nu}{N}\,dx {}=\frac{\EulerGamma@{2N+1-2n}\EulerGamma@{2N+2-2n}2^{2n-2N-1}n!}{\EulerGamma@{2N+2-n}\left|\EulerGamma@{N+1-n+\iunit\nu}\right|^2}\,\Kronecker{m}{n} }}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \int}}  : integral : http://dlmf.nist.gov/1.4#iv
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{e}}}  : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle P_{n}}}  : pseudo Jacobi polynomomal : http://drmf.wmflabs.org/wiki/Definition:pseudoJacobi
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Gamma}}  : Euler's gamma function : http://dlmf.nist.gov/5.2#E1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{i}}}  : imaginary unit : http://dlmf.nist.gov/1.9.i
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \delta_{m,n}}}  : Kronecker delta : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4

Bibliography

Equation in Section 9.9 of KLS.

URL links

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