DLMF:35.7.E5 (Q9816): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:35.7.E5	No description defined

Statements

Defining formula

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

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DLMF:35.7.E5

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

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

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{\displaystyle{\displaystyle\boldsymbol{{0}}<\mathbf{T}<\mathbf{I}}}

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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.m1adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3adec

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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.m1aadec

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Defining formula

{\displaystyle{\displaystyle a}}

C35.S1.XMD1.m1cdec

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Defining formula

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

C35.S1.XMD11.m1cdec

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Defining formula

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

C35.S1.XMD12.m1dec

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Defining formula

{\displaystyle{\displaystyle b}}

C35.S1.XMD2.m1cdec

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Defining formula

{\displaystyle{\displaystyle c}}

C35.S1.XMD3.m1cdec

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Sitelinks

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