DLMF:22.12.E11 (Q7049): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:22.12.E11	No description defined

Statements

Defining formula

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

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DLMF:22.12.E11

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Jacobian elliptic function

Defining formula

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

C22.S2.E4.m3adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aidec

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Defining formula

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

C19.S2.E8.m1ajdec

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Defining formula

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

C4.S14.E1.m2afdec

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Defining formula

{\displaystyle{\displaystyle k}}

C22.S1.XMD4.m1jdec

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Defining formula

{\displaystyle{\displaystyle\tau}}

C22.S1.XMD6.m1jdec

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