DLMF:19.25.E30 (Q6538)

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DLMF:19.25.E30
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    Statements

    Defining formula
    am ⁑ ( u , k ) = R C ⁑ ( cs 2 ⁑ ( u , k ) , ns 2 ⁑ ( u , k ) ) , Jacobi-elliptic-amplitude 𝑒 π‘˜ Carlson-integral-RC Jacobi-elliptic-cs 2 𝑒 π‘˜ Jacobi-elliptic-ns 2 𝑒 π‘˜ {\displaystyle{\displaystyle\operatorname{am}\left(u,k\right)=R_{C}\left({% \operatorname{cs}^{2}}\left(u,k\right),{\operatorname{ns}^{2}}\left(u,k\right)% \right),}}
    0 references
    DLMF id
    DLMF:19.25.E30
    0 references
    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    Defining formula
    R C ⁑ ( x , y ) Carlson-integral-RC π‘₯ 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    xml-id
    C19.S2.E17.m2aadec
    0 references
    Jacobi’s amplitude function
    Defining formula
    am ⁑ ( x , k ) Jacobi-elliptic-amplitude π‘₯ π‘˜ {\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S16.E1.m2adec
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    Jacobian elliptic function
    Defining formula
    cs ⁑ ( z , k ) Jacobi-elliptic-cs 𝑧 π‘˜ {\displaystyle{\displaystyle\operatorname{cs}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E9.m3adec
    0 references
    Jacobian elliptic function
    Defining formula
    ns ⁑ ( z , k ) Jacobi-elliptic-ns 𝑧 π‘˜ {\displaystyle{\displaystyle\operatorname{ns}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m3adec
    0 references
    Q11808
    Defining formula
    k π‘˜ {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1acdec
    0 references
     
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