DLMF:19.25.E4 (Q6508)

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Language	Label	Description	Also known as
English	DLMF:19.25.E4	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\Pi\left(\alpha^{2},k\right)=-\tfrac{1}{3}(k^{2}/% \alpha^{2})R_{J}\left(0,1-k^{2},1,1-(k^{2}/\alpha^{2})\right),}}

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DLMF:19.25.E4

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{\displaystyle{\displaystyle-\infty<k^{2}<1<\alpha^{2}}}

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symmetric elliptic integral of third kind

Defining formula

{\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}% \right)}}

C19.S16.E2.m2aadec

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Defining formula

{\displaystyle{\displaystyle\Pi\left(\NVar{\alpha}^{2},\NVar{k}\right)}}

C19.S2.E8.m4abdec

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Defining formula

{\displaystyle{\displaystyle k}}

C19.S1.XMD5.m1cdec

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