DLMF:22.16.E25 (Q7145)

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Language	Label	Description	Also known as
English	DLMF:22.16.E25	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathcal{E}\left(x,k\right)=-\int_{0}^{x}\left({% \operatorname{ds}^{2}}\left(t,k\right)-t^{-2}\right)\mathrm{d}t+x^{-1}+{k^{% \prime}}^{2}x-\operatorname{cn}\left(x,k\right)\operatorname{ds}\left(x,k% \right),}}

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DLMF:22.16.E25

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Jacobi’s epsilon function

Defining formula

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

C22.S16.E14.m2akdec

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Jacobian elliptic function

Defining formula

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

C22.S2.E5.m2acdec

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Jacobian elliptic function

Defining formula

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

C22.S2.E7.m3aadec

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Defining formula

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

C1.S4.SS4.m1aldec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aldec

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Defining formula

{\displaystyle{\displaystyle x}}

C22.S1.XMD1.m1xdec

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Defining formula

{\displaystyle{\displaystyle k}}

C22.S1.XMD4.m1vdec

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Sitelinks

Wikipedia(0 entries)

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