DLMF:22.14.E15 (Q7090)

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DLMF:22.14.E15
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    Statements

    Defining formula
    ∫ cn ⁡ ( x , k ) ⁢ d x sn 2 ⁡ ( x , k ) = - dn ⁡ ( x , k ) sn ⁡ ( x , k ) . Jacobi-elliptic-cn 𝑥 𝑘 𝑥 Jacobi-elliptic-sn 2 𝑥 𝑘 Jacobi-elliptic-dn 𝑥 𝑘 Jacobi-elliptic-sn 𝑥 𝑘 {\displaystyle{\displaystyle\int\frac{\operatorname{cn}\left(x,k\right)\mathrm% {d}x}{{\operatorname{sn}^{2}}\left(x,k\right)}=-\frac{\operatorname{dn}\left(x% ,k\right)}{\operatorname{sn}\left(x,k\right)}.}}
    0 references
    DLMF id
    DLMF:22.14.E15
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    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.m2addec
    0 references
    Jacobian elliptic function
    Defining formula
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2aedec
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