DLMF:22.6.E6 (Q6940)

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DLMF:22.6.E6
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    test
    cn ⁡ ( 2 ⁢ z , k ) = cn 2 ⁡ ( z , k ) - sn 2 ⁡ ( z , k ) ⁢ dn 2 ⁡ ( z , k ) 1 - k 2 ⁢ sn 4 ⁡ ( z , k ) = cn 4 ⁡ ( z , k ) - k ′ 2 ⁢ sn 4 ⁡ ( z , k ) 1 - k 2 ⁢ sn 4 ⁡ ( z , k ) , Jacobi-elliptic-cn 2 𝑧 𝑘 Jacobi-elliptic-cn 2 𝑧 𝑘 Jacobi-elliptic-sn 2 𝑧 𝑘 Jacobi-elliptic-dn 2 𝑧 𝑘 1 superscript 𝑘 2 Jacobi-elliptic-sn 4 𝑧 𝑘 Jacobi-elliptic-cn 4 𝑧 𝑘 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sn 4 𝑧 𝑘 1 superscript 𝑘 2 Jacobi-elliptic-sn 4 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(2z,k\right)=\frac{{% \operatorname{cn}^{2}}\left(z,k\right)-{\operatorname{sn}^{2}}\left(z,k\right)% {\operatorname{dn}^{2}}\left(z,k\right)}{1-k^{2}{\operatorname{sn}^{4}}\left(z% ,k\right)}=\frac{{\operatorname{cn}^{4}}\left(z,k\right)-{k^{\prime}}^{2}{% \operatorname{sn}^{4}}\left(z,k\right)}{1-k^{2}{\operatorname{sn}^{4}}\left(z,% k\right)},}}
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    DLMF id
    DLMF:22.6.E6
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