DLMF:22.9.E5 (Q6997)

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DLMF:22.9.E5
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    Statements

    Defining formula
    c m , p ( 4 ) = cn ⁡ ( z + 4 ⁢ p - 1 ⁢ ( m - 1 ) ⁢ K ⁡ ( k ) , k ) , superscript subscript 𝑐 𝑚 𝑝 4 Jacobi-elliptic-cn 𝑧 4 superscript 𝑝 1 𝑚 1 complete-elliptic-integral-first-kind-K 𝑘 𝑘 {\displaystyle{\displaystyle c_{m,p}^{(4)}=\operatorname{cn}\left(z+4p^{-1}(m-% 1)K\left(k\right),k\right),}}
    0 references
    DLMF id
    DLMF:22.9.E5
    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.m2aadec
    0 references
    Q11600
    Defining formula
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1addec
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    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.m1ddec
    0 references
    Q11997
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C22.S9.XMD1.m1ddec
    0 references
     
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