DLMF:22.12.E7 (Q7045)

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Language	Label	Description	Also known as
English	DLMF:22.12.E7	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle 2iKk^{\prime}\operatorname{nd}\left(2Kt,k\right)=% \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan\left(\pi(t+\frac{1}{2}% -(n+\frac{1}{2})\tau)\right)}=\lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\lim_{M% \to\infty}\left(\sum_{m=-M}^{M}\frac{1}{t+\frac{1}{2}-m-(n+\frac{1}{2})\tau}% \right),}}

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DLMF:22.12.E7

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Jacobian elliptic function

Defining formula

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

C22.S2.E6.m3adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aedec

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Defining formula

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

C19.S2.E8.m1afdec

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Defining formula

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

C1.S9.E1.m2addec

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tangent function

Defining formula

{\displaystyle{\displaystyle\tan\NVar{z}}}

C4.S14.E4.m2aadec

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Defining formula

{\displaystyle{\displaystyle k}}

C22.S1.XMD4.m1fdec

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Defining formula

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

C22.S1.XMD5.m1adec

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Defining formula

{\displaystyle{\displaystyle\tau}}

C22.S1.XMD6.m1fdec

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