DLMF:22.16.E2 (Q7121)

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DLMF:22.16.E2
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    Statements

    Defining formula
    am ⁡ ( x + 2 ⁢ K , k ) = am ⁡ ( x , k ) + π . Jacobi-elliptic-amplitude 𝑥 2 𝐾 𝑘 Jacobi-elliptic-amplitude 𝑥 𝑘 𝜋 {\displaystyle{\displaystyle\operatorname{am}\left(x+2K,k\right)=\operatorname% {am}\left(x,k\right)+\pi.}}
    0 references
    DLMF id
    DLMF:22.16.E2
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    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.m2aadec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    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
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    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1adec
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