DLMF:22.16.E19 (Q7139)

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Language	Label	Description	Also known as
English	DLMF:22.16.E19	No description defined

Statements

Defining formula

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

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DLMF:22.16.E19

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Jacobi’s epsilon function

Defining formula

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

C22.S16.E14.m2aedec

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Jacobian elliptic function

Defining formula

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

C22.S2.E8.m2aadec

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Jacobian elliptic function

Defining formula

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

C22.S2.E7.m2adec

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Jacobian elliptic function

Defining formula

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

C22.S2.E4.m2aedec

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Defining formula

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

C1.S4.SS4.m1afdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3afdec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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