DLMF:16.5.E3 (Q5214)

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Language	Label	Description	Also known as
English	DLMF:16.5.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{{}_{p+1}F_{q}}\left({a_{0},\dots,a_{p}\atop b_{1}% ,\dots,b_{q}};z\right)=\frac{1}{\Gamma\left(a_{0}\right)}\int_{0}^{\infty}{% \mathrm{e}^{-t}}t^{a_{0}-1}{{}_{p}F_{q}}\left({a_{1},\dots,a_{p}\atop b_{1},% \cdots,b_{q}};zt\right)\mathrm{d}t,}}

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DLMF:16.5.E3

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{\displaystyle{\displaystyle\Re z<1}}

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{\displaystyle{\displaystyle\Re a_{0}>0}}

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2abdec

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Defining formula

{\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}

C16.S2.m1abdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1abdec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aadec

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Defining formula

{\displaystyle{\displaystyle p}}

C16.S1.XMD1.m1bdec

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Defining formula

{\displaystyle{\displaystyle q}}

C16.S1.XMD2.m1bdec

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Defining formula

{\displaystyle{\displaystyle z}}

C16.S1.XMD3.m1bdec

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Defining formula

{\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}

C16.S1.XMD4.m1bdec

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Defining formula

{\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}

C16.S1.XMD5.m1bdec

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Sitelinks

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