DLMF:22.17.E7 (Q7162)

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DLMF:22.17.E7
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    Statements

    Defining formula
    cn ⁡ ( z , i ⁢ k ) = cd ⁡ ( z / k 1 ′ , k 1 ) , Jacobi-elliptic-cn 𝑧 𝑖 𝑘 Jacobi-elliptic-cd 𝑧 superscript subscript 𝑘 1 ′ subscript 𝑘 1 {\displaystyle{\displaystyle\operatorname{cn}\left(z,ik\right)=\operatorname{% cd}\left(z/k_{1}^{\prime},k_{1}\right),}}
    0 references
    DLMF id
    DLMF:22.17.E7
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cd ⁡ ( z , k ) Jacobi-elliptic-cd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E8.m2adec
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    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
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
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    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1edec
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