DLMF:19.25.E14 (Q6518)

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Language	Label	Description	Also known as
English	DLMF:19.25.E14	No description defined

Statements

Defining formula

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

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DLMF:19.25.E14

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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.m2abdec

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Legendre’s incomplete elliptic integral of the first kind

Defining formula

{\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}

C19.S2.E4.m2abdec

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Legendre’s incomplete elliptic integral of the third kind

Defining formula

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

C19.S2.E7.m2adec

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Defining formula

{\displaystyle{\displaystyle\phi}}

C19.S1.XMD4.m1idec

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Defining formula

{\displaystyle{\displaystyle k}}

C19.S1.XMD5.m1mdec

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Defining formula

{\displaystyle{\displaystyle\alpha^{2}}}

C19.S1.XMD7.m1cdec

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