DLMF:22.6.E2 (Q6936)

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DLMF:22.6.E2
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    Statements

    Defining formula
    1 + cs 2 ⁡ ( z , k ) = k 2 + ds 2 ⁡ ( z , k ) = ns 2 ⁡ ( z , k ) , 1 Jacobi-elliptic-cs 2 𝑧 𝑘 superscript 𝑘 2 Jacobi-elliptic-ds 2 𝑧 𝑘 Jacobi-elliptic-ns 2 𝑧 𝑘 {\displaystyle{\displaystyle 1+{\operatorname{cs}^{2}}\left(z,k\right)=k^{2}+{% \operatorname{ds}^{2}}\left(z,k\right)={\operatorname{ns}^{2}}\left(z,k\right)% ,}}
    0 references
    DLMF id
    DLMF:22.6.E2
    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.m3adec
    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.m3adec
    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.m3adec
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    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1adec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1adec
    0 references
     
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