DLMF:35.7.E2 (Q9813): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:35.7.E2	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle P^{(\gamma,\delta)}_{\nu}\left(\mathbf{T}\right)=% \frac{\Gamma_{m}\left(\gamma+\nu+\frac{1}{2}(m+1)\right)}{\Gamma_{m}\left(% \gamma+\frac{1}{2}(m+1)\right)}\*{{}_{2}F_{1}}\left({-\nu,\gamma+\delta+\nu+% \frac{1}{2}(m+1)\atop\gamma+\frac{1}{2}(m+1)};\mathbf{T}\right),}}

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DLMF:35.7.E2

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Symbols defined

Jacobi function of matrix argument

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{\displaystyle{\displaystyle\gamma,\delta,\nu\in\mathbb{C}}}

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{\displaystyle{\displaystyle\Re(\gamma)>-1}}

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

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{\displaystyle{\displaystyle\gamma,\delta,\nu\in\mathbb{C}}}

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{\displaystyle{\displaystyle\Re(\gamma)>-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.m2aadec

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Defining formula

{\displaystyle{\displaystyle\mathbb{C}}}

introduction.Sx4.p1.t1.r1.m2adec

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Defining formula

{\displaystyle{\displaystyle\in}}

introduction.Sx4.p1.t1.r10.m2adec

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Defining formula

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

C35.S3.SS1.m1adec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1adec

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Defining formula

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

C35.S1.XMD11.m1adec

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Sitelinks

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