DLMF:19.22.E20 (Q6466)

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Language	Label	Description	Also known as
English	DLMF:19.22.E20	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle(p_{\pm}^{2}-p_{\mp}^{2})R_{J}\left(x^{2},y^{2},z^% {2},p^{2}\right)=2(p_{\pm}^{2}-a^{2})R_{J}\left(a^{2},z_{+}^{2},z_{-}^{2},p_{% \pm}^{2}\right)-3R_{F}\left(x^{2},y^{2},z^{2}\right)+3R_{C}\left(z^{2},p^{2}% \right),}}

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DLMF:19.22.E20

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Carlson’s combination of inverse circular and inverse hyperbolic functions

Defining formula

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

C19.S2.E17.m2adec

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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.m2ahdec

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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.m2addec

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