DLMF:29.8.E8 (Q8712)

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Language	Label	Description	Also known as
English	DLMF:29.8.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathit{Es}^{2m+1}_{\nu}\left(z_{1},k^{2}\right)% \frac{\left.\ifrac{\mathrm{d}w_{2}(z)}{\mathrm{d}z}\right|_{z=K}+\left.\ifrac{% \mathrm{d}w_{2}(z)}{\mathrm{d}z}\right|_{z=-K}}{\left.\ifrac{\mathrm{d}w_{2}(z% )}{\mathrm{d}z}\right|_{z=0}}=\frac{k^{2}}{k^{\prime}}\operatorname{cn}\left(z% _{1},k\right)\int_{-K}^{K}\operatorname{cn}\left(z,k\right)\frac{\mathrm{d}% \mathsf{P}_{\nu}\left(y\right)}{\mathrm{d}y}\mathit{Es}^{2m+1}_{\nu}\left(z,k^% {2}\right)\mathrm{d}z,}}

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DLMF:29.8.E8

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Jacobian elliptic function

Defining formula

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

C22.S2.E5.m2aadec

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Defining formula

{\displaystyle{\displaystyle\mathit{Es}^{\NVar{m}}_{\NVar{\nu}}\left(\NVar{z},% \NVar{k^{2}}\right)}}

C29.S3.SS4.p1.m6adec

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