DLMF:22.9.E1 (Q6993)

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DLMF:22.9.E1
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    Statements

    Defining formula
    s m , p ( 2 ) = sn ⁡ ( z + 2 ⁢ p - 1 ⁢ ( m - 1 ) ⁢ K ⁡ ( k ) , k ) , superscript subscript 𝑠 𝑚 𝑝 2 Jacobi-elliptic-sn 𝑧 2 superscript 𝑝 1 𝑚 1 complete-elliptic-integral-first-kind-K 𝑘 𝑘 {\displaystyle{\displaystyle s_{m,p}^{(2)}=\operatorname{sn}\left(z+2p^{-1}(m-% 1)K\left(k\right),k\right),}}
    0 references
    DLMF id
    DLMF:22.9.E1
    0 references
    Symbols used
    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.m2adec
    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.m1adec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1dec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1dec
    0 references
    Q11997
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C22.S9.XMD1.m1dec
    0 references
    Q11998
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C22.S9.XMD2.m1dec
    0 references
    Q11999
    Defining formula
    s m , p ( r ) superscript subscript 𝑠 𝑚 𝑝 𝑟 {\displaystyle{\displaystyle s_{m,p}^{(r)}}}
    xml-id
    C22.S9.XMD3.m1dec
    0 references
     
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