DLMF:35.6.E8 (Q9809)

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Language	Label	Description	Also known as
English	DLMF:35.6.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{\boldsymbol{\Omega}}|\mathbf{T}|^{c-\frac{1}% {2}(m+1)}\Psi\left(a;b;\mathbf{T}\right)\mathrm{d}\mathbf{T}=\frac{\Gamma_{m}% \left(c\right)\Gamma_{m}\left(a-c\right)\Gamma_{m}\left(c-b+\frac{1}{2}(m+1)% \right)}{\Gamma_{m}\left(a\right)\Gamma_{m}\left(a-b+\frac{1}{2}(m+1)\right)},}}

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DLMF:35.6.E8

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{\displaystyle{\displaystyle\Re(a)>\Re(c)+\frac{1}{2}(m-1)>m-1}}

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{\displaystyle{\displaystyle\Re(c-b)>-1}}

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confluent hypergeometric function of matrix argument (second kind)

Defining formula

{\displaystyle{\displaystyle\Psi\left(\NVar{a};\NVar{b};\NVar{\mathbf{T}}% \right)}}

C35.S6.E2.m2aadec

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Defining formula

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

C1.S4.SS4.m1addec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3addec

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Defining formula

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

C35.S3.SS1.m1acdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aedec

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Defining formula

{\displaystyle{\displaystyle a}}

C35.S1.XMD1.m1fdec

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Defining formula

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

C35.S1.XMD11.m1gdec

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Defining formula

{\displaystyle{\displaystyle{\boldsymbol{\Omega}}}}

C35.S1.XMD13.m1bdec

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Defining formula

{\displaystyle{\displaystyle b}}

C35.S1.XMD2.m1fdec

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Defining formula

{\displaystyle{\displaystyle c}}

C35.S1.XMD3.m1dec

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Defining formula

{\displaystyle{\displaystyle m}}

C35.S1.XMD8.m1edec

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Sitelinks

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