DLMF:22.17.E6 (Q7161)

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DLMF:22.17.E6
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    Statements

    Defining formula
    sn ⁡ ( z , i ⁢ k ) = k 1 ′ ⁢ sd ⁡ ( z / k 1 ′ , k 1 ) , Jacobi-elliptic-sn 𝑧 𝑖 𝑘 superscript subscript 𝑘 1 ′ Jacobi-elliptic-sd 𝑧 superscript subscript 𝑘 1 ′ subscript 𝑘 1 {\displaystyle{\displaystyle\operatorname{sn}\left(z,ik\right)=k_{1}^{\prime}% \operatorname{sd}\left(z/k_{1}^{\prime},k_{1}\right),}}
    0 references
    DLMF id
    DLMF:22.17.E6
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    sd ⁡ ( z , k ) Jacobi-elliptic-sd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E7.m2adec
    0 references
    Jacobian elliptic function
    Defining formula
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    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
    Q12020
    Defining formula
    k 1 subscript 𝑘 1 {\displaystyle{\displaystyle k_{1}}}
    xml-id
    C22.S17.XMD1.m1adec
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