DLMF:35.8.E13 (Q9835): Difference between revisions

Revision as of 15:02, 2 January 2020

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

{\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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{\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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@@ Property / Symbols used @@
+generalized hypergeometric function of matrix argument
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{\mathbf{T}}\right)}}$ 
\genhyperFmat{\NVar{p}}{\NVar{q}}@{\NVar{a_{1},\dots,a_{p}}}{\NVar{b_{1},\dots,b_{q}}}{\NVar{\mathbf{T}}}
+xml-id: C35.S8.E1.m2aldec