DLMF:22.12.E6 (Q7044)

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Language	Label	Description	Also known as
English	DLMF:22.12.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle-2iKkk^{\prime}\operatorname{sd}\left(2Kt,k\right)% =\sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin\left(\pi(t+\frac{1}{2}-(n+% \frac{1}{2})\tau)\right)}=\sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{% \infty}\frac{(-1)^{m+n}}{t+\frac{1}{2}-m-(n+\frac{1}{2})\tau}\right),}}

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DLMF:22.12.E6

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Jacobian elliptic function

Defining formula

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

C22.S2.E7.m2adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2addec

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Defining formula

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

C19.S2.E8.m1aedec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2acdec

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Defining formula

{\displaystyle{\displaystyle\sin\NVar{z}}}

C4.S14.E1.m2acdec

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Defining formula

{\displaystyle{\displaystyle k}}

C22.S1.XMD4.m1edec

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Defining formula

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

C22.S1.XMD5.m1dec

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Defining formula

{\displaystyle{\displaystyle\tau}}

C22.S1.XMD6.m1edec

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