DLMF:22.6.E8 (Q6942)

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DLMF:22.6.E8
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    Statements

    cd ( 2 z , k ) = cd 2 ( z , k ) - k 2 sd 2 ( z , k ) nd 2 ( z , k ) 1 + k 2 k 2 sd 4 ( z , k ) , Jacobi-elliptic-cd 2 𝑧 𝑘 Jacobi-elliptic-cd 2 𝑧 𝑘 superscript superscript 𝑘 2 Jacobi-elliptic-sd 2 𝑧 𝑘 Jacobi-elliptic-nd 2 𝑧 𝑘 1 superscript 𝑘 2 superscript superscript 𝑘 2 Jacobi-elliptic-sd 4 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(2z,k\right)=\frac{{% \operatorname{cd}^{2}}\left(z,k\right)-{k^{\prime}}^{2}{\operatorname{sd}^{2}}% \left(z,k\right){\operatorname{nd}^{2}}\left(z,k\right)}{1+k^{2}{k^{\prime}}^{% 2}{\operatorname{sd}^{4}}\left(z,k\right)},}}
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    DLMF:22.6.E8
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    cd ( z , k ) Jacobi-elliptic-cd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E8.m2aadec
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    nd ( z , k ) Jacobi-elliptic-nd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nd}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E6.m3aadec
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    sd ( z , k ) Jacobi-elliptic-sd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sd}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E7.m2aadec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C22.S1.XMD3.m1gdec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C22.S1.XMD4.m1gdec
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    k superscript 𝑘 {\displaystyle{\displaystyle k^{\prime}}}
    C22.S1.XMD5.m1ddec
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