DLMF:35.8.E13 (Q9835)

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No description defined

Language	Label	Description	Also known as
English	DLMF:35.8.E13	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int\limits_{\boldsymbol{{0}}<\mathbf{X}<\mathbf{I% }}|\mathbf{X}|^{a_{1}-\frac{1}{2}(m+1)}{|\mathbf{I}-\mathbf{X}|}^{b_{1}-a_{1}-% \frac{1}{2}(m+1)}\*{{}_{p}F_{q}}\left({a_{2},\dots,a_{p+1}\atop b_{2},\dots,b_% {q+1}};\mathbf{T}\mathbf{X}\right)\mathrm{d}\mathbf{X}=\frac{1}{\mathrm{B}_{m}% \left(b_{1}-a_{1},a_{1}\right)}{{}_{p+1}F_{q+1}}\left({a_{1},\dots,a_{p+1}% \atop b_{1},\dots,b_{q+1}};\mathbf{T}\right),}}

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DLMF:35.8.E13

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{\displaystyle{\displaystyle\Re(b_{1}-a_{1}),\Re(a_{1})>\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.m2aldec

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Defining formula

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

C1.S4.SS4.m1aadec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aadec

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multivariate beta function

Defining formula

{\displaystyle{\displaystyle\mathrm{B}_{\NVar{m}}\left(\NVar{a},\NVar{b}\right% )}}

C35.S3.E3.m2adec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1acdec

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Defining formula

{\displaystyle{\displaystyle a}}

C35.S1.XMD1.m1jdec

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Defining formula

{\displaystyle{\displaystyle\mathbf{T}}}

C35.S1.XMD11.m1hdec

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Defining formula

{\displaystyle{\displaystyle\mathbf{X}}}

C35.S1.XMD12.m1adec

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Defining formula

{\displaystyle{\displaystyle b}}

C35.S1.XMD2.m1jdec

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Defining formula

{\displaystyle{\displaystyle p}}

C35.S1.XMD6.m1fdec

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Defining formula

{\displaystyle{\displaystyle q}}

C35.S1.XMD7.m1fdec

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Defining formula

{\displaystyle{\displaystyle m}}

C35.S1.XMD8.m1fdec

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