DLMF:22.16.E33 (Q7153)

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Language	Label	Description	Also known as
English	DLMF:22.16.E33	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathrm{Z}\left(x+K|k\right)=\mathrm{Z}\left(x|k% \right)-k^{2}\operatorname{sn}\left(x,k\right)\operatorname{cd}\left(x,k\right% ),}}

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DLMF:22.16.E33

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Jacobi’s zeta function

Defining formula

{\displaystyle{\displaystyle\mathrm{Z}\left(\NVar{x}|\NVar{k}\right)}}

C22.S16.E32.m2aadec

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Jacobian elliptic function

Defining formula

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

C22.S2.E8.m2addec

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Jacobian elliptic function

Defining formula

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

C22.S2.E4.m2aldec

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Defining formula

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

C19.S2.E8.m1agdec

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Defining formula

{\displaystyle{\displaystyle x}}

C22.S1.XMD1.m1afdec

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Sitelinks

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