DLMF:16.2.E5 (Q5187): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:16.2.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{{}_{p}{\mathbf{F}}_{q}}\left(\mathbf{a};\mathbf{b% };z\right)=\ifrac{{{}_{p}F_{q}}\left({a_{1},\dots,a_{p}\atop b_{1},\dots,b_{q}% };z\right)}{\left(\Gamma\left(b_{1}\right)\cdots\Gamma\left(b_{q}\right)\right% )}=\sum_{k=0}^{\infty}\frac{{\left(a_{1}\right)_{k}}\cdots{\left(a_{p}\right)_% {k}}}{\Gamma\left(b_{1}+k\right)\cdots\Gamma\left(b_{q}+k\right)}\frac{z^{k}}{% k!};}}

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DLMF:16.2.E5

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Symbols defined

scaled (or Olver’s) generalized hypergeometric function

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Defining formula

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

C5.S2.E1.m2adec

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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.m1acdec

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Defining formula

{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

C5.S2.SS3.m1acdec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5abdec

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Defining formula

{\displaystyle{\displaystyle p}}

C16.S1.XMD1.m1cdec

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Defining formula

{\displaystyle{\displaystyle q}}

C16.S1.XMD2.m1ddec

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Defining formula

{\displaystyle{\displaystyle z}}

C16.S1.XMD3.m1cdec

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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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