DLMF:19.25.E11 (Q6515)

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Language	Label	Description	Also known as
English	DLMF:19.25.E11	No description defined

Statements

Defining formula

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

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DLMF:19.25.E11

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{\displaystyle{\displaystyle\phi\neq\tfrac{1}{2}\pi}}

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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.m2addec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.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.m2addec

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Defining formula

{\displaystyle{\displaystyle\phi}}

C19.S1.XMD4.m1fdec

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Defining formula

{\displaystyle{\displaystyle k}}

C19.S1.XMD5.m1jdec

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Defining formula

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

C19.S1.XMD6.m1ddec

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