Formula:KLS:01.06:01

<< The binomial theorem and other summation formulas

formula in Some integrals

Formula:KLS:01.06:02 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \index{Euler's integral representation for a $\HyperpFq{2}{1}$}\index{Hypergeometric function!Euler's integral representation} \HyperpFq{2}{1}@@{a,b}{c}{z}=\frac{\EulerGamma@{c}}{\EulerGamma@{b}\EulerGamma@{c-b}} \int_0^1t^{b-1}(1-t)^{c-b-1}(1-zt)^{-a}\,dt }}

Proof

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Symbols List

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 \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

Bibliography

Equation in Section 1.6 of KLS.

URL links

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<< The binomial theorem and other summation formulas

formula in Some integrals

Formula:KLS:01.06:02 >>