DLMF:22.14.E3 (Q7078)

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DLMF:22.14.E3
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    Statements

    Defining formula
    ∫ dn ⁡ ( x , k ) ⁢ d x = Arcsin ⁡ ( sn ⁡ ( x , k ) ) = am ⁡ ( x , k ) . Jacobi-elliptic-dn 𝑥 𝑘 𝑥 multivalued-inverse-sine Jacobi-elliptic-sn 𝑥 𝑘 Jacobi-elliptic-amplitude 𝑥 𝑘 {\displaystyle{\displaystyle\int\operatorname{dn}\left(x,k\right)\mathrm{d}x=% \operatorname{Arcsin}\left(\operatorname{sn}\left(x,k\right)\right)=% \operatorname{am}\left(x,k\right).}}
    0 references
    DLMF id
    DLMF:22.14.E3
    0 references
    Symbols used
    Jacobi’s amplitude function
    Defining formula
    am ⁡ ( x , k ) Jacobi-elliptic-amplitude 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S16.E1.m2adec
    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.m2abdec
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    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.m2aadec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
     
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