Formula:5911

Digital Library of Mathematical Functions ID 16.5.E3

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \genhyperF{p+1}{q}@@{a_{0},\dots,a_{p}}{b_{1},\dots,b_{q}}{z}=\frac{1}{\EulerGamma@{a_{0}}}\int_{0}^{\infty}\expe^{-t}t^{a_{0}-1}\genhyperF{p}{q}@@{a_{1},\dots,a_{p}}{b_{1},\cdots,b_{q}}{zt}\diff{t},}

Constraint(s)

${\displaystyle{\displaystyle\Re z<1}}$
${\displaystyle{\displaystyle\Re a_{0}>0}}$

Symbols List

• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \EulerGamma@{\NVar{z}}} : gamma function
• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \genhyperF{\NVar{p}}{\NVar{q}}@{\NVar{a_{1},\dots,a_{p}}}{\NVar{b_{1},\dots,b_{q}}}{\NVar{z}}} : alternatively F q p ( a ; b ; z ) or F q p ( a b ; z ) generalized hypergeometric function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \expe} : base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle p}}$: nonnegative integer
• ${\displaystyle{\displaystyle q}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}$: real or complex parameters
• ${\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}$: real or complex parameters
 

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