DLMF:22.6.E14 (Q6948)

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DLMF:22.6.E14
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    Statements

    Defining formula
    ns ⁡ ( 2 ⁢ z , k ) = ns 4 ⁡ ( z , k ) - k 2 2 ⁢ cs ⁡ ( z , k ) ⁢ ds ⁡ ( z , k ) ⁢ ns ⁡ ( z , k ) , Jacobi-elliptic-ns 2 𝑧 𝑘 Jacobi-elliptic-ns 4 𝑧 𝑘 superscript 𝑘 2 2 Jacobi-elliptic-cs 𝑧 𝑘 Jacobi-elliptic-ds 𝑧 𝑘 Jacobi-elliptic-ns 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{ns}\left(2z,k\right)=\frac{{% \operatorname{ns}^{4}}\left(z,k\right)-k^{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.E14
    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.m3aadec
    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.m3aadec
    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.m3aadec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1mdec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1mdec
    0 references
     
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