DLMF:22.7.E7 (Q6964)

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DLMF:22.7.E7
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    Statements

    Defining formula
    cn ⁡ ( z , k ) = ( 1 + k 2 ′ ) ⁢ ( dn 2 ⁡ ( z / ( 1 + k 2 ′ ) , k 2 ) - k 2 ′ ) k 2 2 ⁢ dn ⁡ ( z / ( 1 + k 2 ′ ) , k 2 ) , Jacobi-elliptic-cn 𝑧 𝑘 1 superscript subscript 𝑘 2 ′ Jacobi-elliptic-dn 2 𝑧 1 superscript subscript 𝑘 2 ′ subscript 𝑘 2 superscript subscript 𝑘 2 ′ superscript subscript 𝑘 2 2 Jacobi-elliptic-dn 𝑧 1 superscript subscript 𝑘 2 ′ subscript 𝑘 2 {\displaystyle{\displaystyle\operatorname{cn}\left(z,k\right)=\frac{(1+k_{2}^{% \prime})({\operatorname{dn}^{2}}\left(z/(1+k_{2}^{\prime}),k_{2}\right)-k_{2}^% {\prime})}{k_{2}^{2}\operatorname{dn}\left(z/(1+k_{2}^{\prime}),k_{2}\right)},}}
    0 references
    DLMF id
    DLMF:22.7.E7
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cn ⁡ ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m2abdec
    0 references
    Jacobian elliptic function
    Defining formula
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2acdec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1ddec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1edec
    0 references
    Q11989
    Defining formula
    k 2 subscript 𝑘 2 {\displaystyle{\displaystyle k_{2}}}
    xml-id
    C22.S7.XMD2.m1bdec
    0 references
    Q11990
    Defining formula
    k 2 ′ superscript subscript 𝑘 2 ′ {\displaystyle{\displaystyle k_{2}^{\prime}}}
    xml-id
    C22.S7.XMD3.m1bdec
    0 references
     
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