DLMF:22.15.E11 (Q7106)

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DLMF:22.15.E11
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    Statements

    Defining formula
    x = ∫ 0 sn ⁡ ( x , k ) d t ( 1 - t 2 ) ⁢ ( 1 - k 2 ⁢ t 2 ) , 𝑥 superscript subscript 0 Jacobi-elliptic-sn 𝑥 𝑘 𝑡 1 superscript 𝑡 2 1 superscript 𝑘 2 superscript 𝑡 2 {\displaystyle{\displaystyle x=\int_{0}^{\operatorname{sn}\left(x,k\right)}% \frac{\mathrm{d}t}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}},}}
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    DLMF id
    DLMF:22.15.E11
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    constraint
    0 ≤ k ≤ 1 0 𝑘 1 {\displaystyle{\displaystyle 0\leq k\leq 1}}
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    Symbols used
    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.m1adec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
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    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1jdec
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    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1jdec
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