DLMF:19.20.E13 (Q6398)

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Language	Label	Description	Also known as
English	DLMF:19.20.E13	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle 2(p-x)R_{J}\left(x,y,z,p\right)=3R_{F}\left(x,y,z% \right)-3\sqrt{x}R_{C}\left(yz,p^{2}\right),}}

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DLMF:19.20.E13

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{\displaystyle{\displaystyle p=x\pm\sqrt{(y-x)(z-x)}}}

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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.m2addec

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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.m2aedec

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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.m2agdec

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