DLMF:19.25.E7 (Q6511)

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Language	Label	Description	Also known as
English	DLMF:19.25.E7	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle E\left(\phi,k\right)=2R_{G}\left(c-1,c-k^{2},c% \right)-(c-1)R_{F}\left(c-1,c-k^{2},c\right)-\sqrt{(c-1)(c-k^{2})/c},}}

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DLMF:19.25.E7

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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.m2abdec

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symmetric elliptic integral of second kind

Defining formula

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

C19.S16.E3.m2aadec

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Legendre’s incomplete elliptic integral of the second kind

Defining formula

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

C19.S2.E5.m2adec

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Defining formula

{\displaystyle{\displaystyle\phi}}

C19.S1.XMD4.m1bdec

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Defining formula

{\displaystyle{\displaystyle k}}

C19.S1.XMD5.m1fdec

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