DLMF:22.12.E2 (Q7040): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:22.12.E2	No description defined

Statements

Defining formula

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

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DLMF:22.12.E2

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Jacobian elliptic function

Defining formula

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

C22.S2.E4.m2adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

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Defining formula

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

C19.S2.E8.m1aadec

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Defining formula

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

C4.S14.E1.m2adec

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