Formula:KLS:01.06:02

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \index{Barnes' integral representation}\index{Hypergeometric function!Barnes' integral representation} \frac{\EulerGamma@{a}\EulerGamma@{b}}{\EulerGamma@{c}}\,\HyperpFq{2}{1}@@{a,b}{c}{z}=\frac{1}{2\cpi \iunit} \int_{-\iunit\infty}^{\iunit\infty}\frac{\EulerGamma@{a+s}\EulerGamma@{b+s}\EulerGamma@{-s}}{\EulerGamma@{c+s}}(-z)^s\,ds }}

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 {{}_{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 \pi}}  : ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
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

Bibliography

Equation in Section 1.6 of KLS.

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