DLMF:22.7.E8 (Q6965)

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DLMF:22.7.E8
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    dn ( z , k ) = ( 1 - k 2 ) ( dn 2 ( z / ( 1 + k 2 ) , k 2 ) + k 2 ) k 2 2 dn ( z / ( 1 + k 2 ) , k 2 ) . Jacobi-elliptic-dn 𝑧 𝑘 1 superscript subscript 𝑘 2 Jacobi-elliptic-dn 2 𝑧 1 superscript subscript 𝑘 2 subscript 𝑘 2 superscript subscript 𝑘 2 superscript subscript 𝑘 2 2 Jacobi-elliptic-dn 𝑧 1 superscript subscript 𝑘 2 subscript 𝑘 2 {\displaystyle{\displaystyle\operatorname{dn}\left(z,k\right)=\frac{(1-k_{2}^{% \prime})({\operatorname{dn}^{2}}\left(z/(1+k_{2}^{\prime}),k_{2}\right)+k_{2}^% {\prime})}{k_{2}^{2}\operatorname{dn}\left(z/(1+k_{2}^{\prime}),k_{2}\right)}.}}
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    DLMF:22.7.E8
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