DLMF:22.6.E16 (Q6950)

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DLMF:22.6.E16
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    Statements

    Defining formula
    cs ⁡ ( 2 ⁢ z , k ) = cs 4 ⁡ ( z , k ) - k ′ 2 2 ⁢ cs ⁡ ( z , k ) ⁢ ds ⁡ ( z , k ) ⁢ ns ⁡ ( z , k ) . Jacobi-elliptic-cs 2 𝑧 𝑘 Jacobi-elliptic-cs 4 𝑧 𝑘 superscript superscript 𝑘 ′ 2 2 Jacobi-elliptic-cs 𝑧 𝑘 Jacobi-elliptic-ds 𝑧 𝑘 Jacobi-elliptic-ns 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cs}\left(2z,k\right)=\frac{{% \operatorname{cs}^{4}}\left(z,k\right)-{k^{\prime}}^{2}}{2\operatorname{cs}% \left(z,k\right)\operatorname{ds}\left(z,k\right)\operatorname{ns}\left(z,k% \right)}.}}
    0 references
    DLMF id
    DLMF:22.6.E16
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cs ⁡ ( z , k ) Jacobi-elliptic-cs 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cs}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E9.m3acdec
    0 references
    Jacobian elliptic function
    Defining formula
    ds ⁡ ( z , k ) Jacobi-elliptic-ds 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{ds}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E7.m3acdec
    0 references
    Jacobian elliptic function
    Defining formula
    ns ⁡ ( z , k ) Jacobi-elliptic-ns 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{ns}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m3acdec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1odec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1odec
    0 references
     
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