Formula:KLS:09.08:40

<< Formula:KLS:09.08:39

formula in Jacobi: Special cases

Formula:KLS:09.08:41 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \frac{\EulerGamma@{\lambda+1}}{\EulerGamma@{\lambda+\frac12} \EulerGamma@{\frac12}} \int_{-1}^1 \frac{\Ultra{\lambda}{n}@{y}}{\Ultra{\lambda}{n}@{1}} (1-y^2)^{\lambda-\frac12} \expe^{\iunit xy} dy =\iunit^n 2^\lambda \EulerGamma@{\lambda+1} x^{-\lambda} \BesselJ{\lambda+n}@{x} }}

Proof

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Symbols List

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 \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 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{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 \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 J_{\nu}}}  : Bessel function of the first kind : http://dlmf.nist.gov/10.2#E2

Bibliography

Equation in Section 9.8 of KLS.

URL links

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<< Formula:KLS:09.08:39

formula in Jacobi: Special cases

Formula:KLS:09.08:41 >>