DLMF:19.16.E12 (Q6328)

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Language	Label	Description	Also known as
English	DLMF:19.16.E12	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle R_{-a}\left(b_{1},\dots,b_{4};c-1,c-k^{2},c,c-% \alpha^{2}\right)=\frac{2({\sin^{2}}\phi)^{1-a^{\prime}}}{\mathrm{B}\left(a,a^% {\prime}\right)}\int_{0}^{\phi}(\sin\theta)^{2a-1}{({\sin^{2}}\phi-{\sin^{2}}% \theta)}^{a^{\prime}-1}\*(\cos\theta)^{1-2b_{1}}{(1-k^{2}{\sin^{2}}\theta)}^{-% b_{2}}{(1-\alpha^{2}{\sin^{2}}\theta)}^{-b_{4}}\mathrm{d}\theta,}}

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DLMF:19.16.E12

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multivariate hypergeometric function

Defining formula

{\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}% };\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}

C19.S16.E9.m2acdec

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Defining formula

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

C5.S12.E1.m2aadec

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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2aadec

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Defining formula

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

C1.S4.SS4.m1afdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3afdec

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Defining formula

{\displaystyle{\displaystyle\sin\NVar{z}}}

C4.S14.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle\phi}}

C19.S1.XMD4.m1adec

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Defining formula

{\displaystyle{\displaystyle k}}

C19.S1.XMD5.m1dec

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Defining formula

{\displaystyle{\displaystyle\alpha^{2}}}

C19.S1.XMD7.m1dec

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