DLMF:19.21.E6 (Q6424)

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Language	Label	Description	Also known as
English	DLMF:19.21.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle(\sqrt{rp}/z)R_{J}\left(0,y,z,p\right)={(r-1)}R_{F% }\left(0,y,z\right)R_{D}\left(p,rz,z\right)+R_{D}\left(0,y,z\right)R_{F}\left(% p,rz,z\right),}}

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DLMF:19.21.E6

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{\displaystyle{\displaystyle r=(y-p)/(y-z)>0}}

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elliptic integral symmetric in only two variables

Defining formula

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

C19.S16.E5.m2acdec

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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.m2adec

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