DLMF:35.8.E5 (Q9827)

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Language	Label	Description	Also known as
English	DLMF:35.8.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a_{1},a_{2},a_{3}\atop b_{1},b% _{2}};\mathbf{I}\right)=\frac{\Gamma_{m}\left(b_{2}\right)\Gamma_{m}\left(c% \right)}{\Gamma_{m}\left(b_{2}-a_{3}\right)\Gamma_{m}\left(c+a_{3}\right)}\*{{% }_{3}F_{2}}\left({b_{1}-a_{1},b_{1}-a_{2},a_{3}\atop b_{1},c+a_{3}};\mathbf{I}% \right),}}

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DLMF:35.8.E5

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{\displaystyle{\displaystyle\Re(b_{2}),\Re(c)>\frac{1}{2}(m-1)}}

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generalized hypergeometric function of matrix argument

Defining formula

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

C35.S8.E1.m2addec

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Defining formula

{\displaystyle{\displaystyle\Gamma_{\NVar{m}}\left(\NVar{a}\right)}}

C35.S3.SS1.m1aadec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1adec

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Defining formula

{\displaystyle{\displaystyle a}}

C35.S1.XMD1.m1bdec

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Defining formula

{\displaystyle{\displaystyle b}}

C35.S1.XMD2.m1bdec

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Defining formula

{\displaystyle{\displaystyle c}}

C35.S1.XMD3.m1dec

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