DLMF:22.16.E19 (Q7139)

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DLMF:22.16.E19
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    ( x , k ) = k 2 k 2 0 x sd 2 ( t , k ) d t + k 2 x + k 2 sn ( x , k ) cd ( x , k ) , Jacobi-Epsilon 𝑥 𝑘 superscript 𝑘 2 superscript superscript 𝑘 2 superscript subscript 0 𝑥 Jacobi-elliptic-sd 2 𝑡 𝑘 𝑡 superscript superscript 𝑘 2 𝑥 superscript 𝑘 2 Jacobi-elliptic-sn 𝑥 𝑘 Jacobi-elliptic-cd 𝑥 𝑘 {\displaystyle{\displaystyle\mathcal{E}\left(x,k\right)=k^{2}{k^{\prime}}^{2}% \int_{0}^{x}{\operatorname{sd}^{2}}\left(t,k\right)\mathrm{d}t+{k^{\prime}}^{2% }x+k^{2}\operatorname{sn}\left(x,k\right)\operatorname{cd}\left(x,k\right),}}
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    DLMF:22.16.E19
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