DLMF:35.8.E12 (Q9834): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:35.8.E12	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{\int_{\boldsymbol{\Omega}}\mathrm{etr}\left(-% \mathbf{T}\mathbf{X}\right)|\mathbf{X}|^{\gamma-\frac{1}{2}(m+1)}\*{{}_{p}F_{q% }}\left({a_{1},\dots,a_{p}\atop b_{1},\dots,b_{q}};-\mathbf{X}\right)\mathrm{d% }\mathbf{X}}=\Gamma_{m}\left(\gamma\right)|\mathbf{T}|^{-\gamma}{{}_{p+1}F_{q}% }\left({a_{1},\dots,a_{p},\gamma\atop b_{1},\dots,b_{q}};-\mathbf{T}^{-1}% \right),}}

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DLMF:35.8.E12

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{\displaystyle{\displaystyle\Re(\gamma)>\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.m2akdec

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Defining formula

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

C1.S4.SS4.m1adec

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Defining formula

{\displaystyle{\displaystyle\mathrm{etr}\left(\NVar{\mathbf{X}}\right)}}

C35.S1.p3.t1.r10.m3aadec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3adec

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Defining formula

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

C35.S3.SS1.m1addec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1abdec

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