DLMF:22.6.E9 (Q6943)

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DLMF:22.6.E9
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    sd ( 2 z , k ) = 2 sd ( z , k ) cd ( z , k ) nd ( z , k ) 1 + k 2 k 2 sd 4 ( z , k ) , Jacobi-elliptic-sd 2 𝑧 𝑘 2 Jacobi-elliptic-sd 𝑧 𝑘 Jacobi-elliptic-cd 𝑧 𝑘 Jacobi-elliptic-nd 𝑧 𝑘 1 superscript 𝑘 2 superscript superscript 𝑘 2 Jacobi-elliptic-sd 4 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sd}\left(2z,k\right)=\frac{2% \operatorname{sd}\left(z,k\right)\operatorname{cd}\left(z,k\right)% \operatorname{nd}\left(z,k\right)}{1+k^{2}{k^{\prime}}^{2}{\operatorname{sd}^{% 4}}\left(z,k\right)},}}
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    DLMF:22.6.E9
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