DLMF:35.6.E6 (Q9807)

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Language	Label	Description	Also known as
English	DLMF:35.6.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathrm{B}_{m}\left(b_{1},b_{2}\right)|\mathbf{T}|% ^{b_{1}+b_{2}-\frac{1}{2}(m+1)}{{}_{1}F_{1}}\left({a_{1}+a_{2}\atop b_{1}+b_{2% }};\mathbf{T}\right)=\int_{\boldsymbol{{0}}<\mathbf{X}<\mathbf{T}}|\mathbf{X}|% ^{b_{1}-\frac{1}{2}(m+1)}{{}_{1}F_{1}}\left({a_{1}\atop b_{1}};\mathbf{X}% \right){|\mathbf{T}-\mathbf{X}|}^{b_{2}-\frac{1}{2}(m+1)}{{}_{1}F_{1}}\left({a% _{2}\atop b_{2}};\mathbf{T}-\mathbf{X}\right)\mathrm{d}\mathbf{X},}}

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DLMF:35.6.E6

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{\displaystyle{\displaystyle\Re(b_{1}),\Re(b_{2})>\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\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1acdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3acdec

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multivariate beta function

Defining formula

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

C35.S3.E3.m2aadec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1addec

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Defining formula

{\displaystyle{\displaystyle a}}

C35.S1.XMD1.m1ddec

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Defining formula

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

C35.S1.XMD11.m1edec

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Sitelinks

Wikipedia(0 entries)

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