DLMF:19.25.E10 (Q6514)

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Language	Label	Description	Also known as
English	DLMF:19.25.E10	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle E\left(\phi,k\right)={k^{\prime}}^{2}R_{F}\left(c% -1,c-k^{2},c\right)+\tfrac{1}{3}k^{2}{k^{\prime}}^{2}R_{D}\left(c-1,c,c-k^{2}% \right)+k^{2}\sqrt{(c-1)/(c(c-k^{2}))},}}

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DLMF:19.25.E10

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{\displaystyle{\displaystyle c>k^{2}}}

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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.m2addec

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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.m2acdec

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Defining formula

{\displaystyle{\displaystyle\phi}}

C19.S1.XMD4.m1edec

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Defining formula

{\displaystyle{\displaystyle k}}

C19.S1.XMD5.m1idec

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Defining formula

{\displaystyle{\displaystyle k^{\prime}}}

C19.S1.XMD6.m1cdec

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