DLMF:22.16.E26 (Q7146)

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Language	Label	Description	Also known as
English	DLMF:22.16.E26	No description defined

Statements

Defining formula

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

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DLMF:22.16.E26

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Jacobi’s epsilon function

Defining formula

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

C22.S16.E14.m2aldec

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Jacobian elliptic function

Defining formula

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

C22.S2.E5.m2addec

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Jacobian elliptic function

Defining formula

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

C22.S2.E9.m3adec

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Jacobian elliptic function

Defining formula

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

C22.S2.E7.m3abdec

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Defining formula

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

C1.S4.SS4.m1amdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3amdec

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Defining formula

{\displaystyle{\displaystyle x}}

C22.S1.XMD1.m1ydec

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Defining formula

{\displaystyle{\displaystyle k}}

C22.S1.XMD4.m1wdec

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