DLMF:22.16.E30 (Q7150)

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Language	Label	Description	Also known as
English	DLMF:22.16.E30	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathcal{E}\left(x,k\right)=\frac{1}{{\theta_{3}^{% 2}}\left(0,q\right)\theta_{4}\left(\xi,q\right)}\frac{\mathrm{d}}{\mathrm{d}% \xi}\theta_{4}\left(\xi,q\right)+\frac{E\left(k\right)}{K\left(k\right)}x,}}

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DLMF:22.16.E30

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Jacobi’s epsilon function

Defining formula

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

C22.S16.E14.m2apdec

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Defining formula

{\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}

C20.S2.SS1.m2adec

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Defining formula

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

C19.S2.E8.m1addec

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Defining formula

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

C19.S2.E8.m2abdec

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derivative of $$f$$ with respect to $$x$$

Defining formula

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

C1.S4.E4.m2adec

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Defining formula

{\displaystyle{\displaystyle q}}

C22.S2.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle x}}

C22.S1.XMD1.m1acdec

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Defining formula

{\displaystyle{\displaystyle k}}

C22.S1.XMD4.m1aadec

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