DLMF:19.22.E7 (Q6445)

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Language	Label	Description	Also known as
English	DLMF:19.22.E7	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle 2p^{2}R_{J}\left(0,x^{2},y^{2},p^{2}\right)=v_{+}% v_{-}R_{J}\left(0,xy,a^{2},v^{2}_{+}\right)+3R_{F}\left(0,xy,a^{2}\right),}}

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DLMF:19.22.E7

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{\displaystyle{\displaystyle v_{\pm}=(p^{2}\pm xy)/(2p)}}

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symmetric elliptic integral of first kind

Defining formula

{\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}

C19.S16.E1.m2addec

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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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