DLMF:29.8.E7 (Q8711)

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Language	Label	Description	Also known as
English	DLMF:29.8.E7	No description defined

Statements

Defining formula

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

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DLMF:29.8.E7

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Jacobian elliptic function

Defining formula

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

C22.S2.E4.m2aadec

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Defining formula

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

C29.S3.SS4.p1.m5aadec

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Defining formula

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

C19.S2.E8.m1acdec

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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.m2aadec

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Defining formula

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

C1.S4.SS4.m1abdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abdec

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Defining formula

{\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=% \mathsf{P}^{0}_{\nu}\left(x\right)}}

C14.S2.SS2.p2.m2abdec

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Defining formula

{\displaystyle{\displaystyle m}}

C29.S1.XMD1.m1adec

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Defining formula

{\displaystyle{\displaystyle y}}

C29.S1.XMD5.m1bdec

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Defining formula

{\displaystyle{\displaystyle z}}

C29.S1.XMD6.m1edec

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Defining formula

{\displaystyle{\displaystyle k}}

C29.S1.XMD8.m1edec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C29.S1.XMD9.m1bdec

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Defining formula

{\displaystyle{\displaystyle w(z)}}

C29.S8.XMD1.m1ddec

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