DLMF:22.9.E6 (Q6998)

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DLMF:22.9.E6
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    Statements

    test
    d m , p ( 4 ) = dn ⁡ ( z + 4 ⁢ p - 1 ⁢ ( m - 1 ) ⁢ K ⁡ ( k ) , k ) . superscript subscript 𝑑 𝑚 𝑝 4 Jacobi-elliptic-dn 𝑧 4 superscript 𝑝 1 𝑚 1 complete-elliptic-integral-first-kind-K 𝑘 𝑘 {\displaystyle{\displaystyle d_{m,p}^{(4)}=\operatorname{dn}\left(z+4p^{-1}(m-% 1)K\left(k\right),k\right).}}
    0 references
    DLMF id
    DLMF:22.9.E6
    0 references
    Symbols used
    Jacobian elliptic function
    test
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2aadec
    0 references
    Q11600
    test
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1aedec
    0 references
     
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