DLMF:22.6.E11 (Q6945)

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DLMF:22.6.E11
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    Statements

    test
    dc ⁡ ( 2 ⁢ z , k ) = dc 2 ⁡ ( z , k ) + k ′ 2 ⁢ sc 2 ⁡ ( z , k ) ⁢ nc 2 ⁡ ( z , k ) 1 - k ′ 2 ⁢ sc 4 ⁡ ( z , k ) , Jacobi-elliptic-dc 2 𝑧 𝑘 Jacobi-elliptic-dc 2 𝑧 𝑘 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sc 2 𝑧 𝑘 Jacobi-elliptic-nc 2 𝑧 𝑘 1 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sc 4 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dc}\left(2z,k\right)=\frac{{% \operatorname{dc}^{2}}\left(z,k\right)+{k^{\prime}}^{2}{\operatorname{sc}^{2}}% \left(z,k\right){\operatorname{nc}^{2}}\left(z,k\right)}{1-{k^{\prime}}^{2}{% \operatorname{sc}^{4}}\left(z,k\right)},}}
    0 references
    DLMF id
    DLMF:22.6.E11
    0 references
    Symbols used
    Jacobian elliptic function
    test
    dc ⁡ ( z , k ) Jacobi-elliptic-dc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E8.m3aadec
    0 references
    Jacobian elliptic function
    test
    nc ⁡ ( z , k ) Jacobi-elliptic-nc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m3aadec
    0 references
    Jacobian elliptic function
    test
    sc ⁡ ( z , k ) Jacobi-elliptic-sc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E9.m2aadec
    0 references
    Q11985
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1jdec
    0 references
     
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