Formula:KLS:01.02:12

<< Formula:KLS:01.02:11

formula in The gamma and beta function

The gamma and beta function >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \frac{1}{2\cpi}\int_{-\infty}^{\infty}\frac{dt}{(r+\iunit t)^{\rho}(s-\iunit t)^{\sigma}} =\frac{(r+s)^{1-\rho-\sigma}\EulerGamma@{\rho+\sigma-1}}{\EulerGamma@{\rho}\EulerGamma@{\sigma}} }}

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{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 \Gamma}}  : Euler's gamma function : http://dlmf.nist.gov/5.2#E1

Bibliography

Equation in Section 1.2 of KLS.

URL links

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<< Formula:KLS:01.02:11

formula in The gamma and beta function

The gamma and beta function >>