DLMF:22.16.E20 (Q7140): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:22.16.E20	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathcal{E}\left(x,k\right)={k^{\prime}}^{2}\int_{% 0}^{x}{\operatorname{nd}^{2}}\left(t,k\right)\mathrm{d}t+k^{2}\operatorname{sn% }\left(x,k\right)\operatorname{cd}\left(x,k\right).}}

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DLMF:22.16.E20

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Jacobi’s epsilon function

Defining formula

{\displaystyle{\displaystyle\mathcal{E}\left(\NVar{x},\NVar{k}\right)}}

C22.S16.E14.m2afdec

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Jacobian elliptic function

Defining formula

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

C22.S2.E8.m2abdec

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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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Jacobian elliptic function

Defining formula

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

C22.S2.E4.m2afdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1agdec

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Sitelinks

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