DLMF:22.11.E13 (Q7037)

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Language	Label	Description	Also known as
English	DLMF:22.11.E13	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{\operatorname{sn}^{2}}\left(z,k\right)=\frac{1}{k% ^{2}}\left(1-\frac{E}{K}\right)-\frac{2\pi^{2}}{k^{2}K^{2}}\sum_{n=1}^{\infty}% \frac{nq^{n}}{1-q^{2n}}\cos\left(2n\zeta\right).}}

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DLMF:22.11.E13

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Jacobian elliptic function

Defining formula

{\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}

C22.S2.E4.m2aadec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aldec

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Defining formula

{\displaystyle{\displaystyle K\left(\NVar{k}\right)}}

C19.S2.E8.m1aldec

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Defining formula

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

C19.S2.E8.m2adec

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