DLMF:22.15.E13 (Q7108)

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DLMF:22.15.E13
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    Statements

    Defining formula
    arccn ⁡ ( x , k ) = ∫ x 1 d t ( 1 - t 2 ) ⁢ ( k ′ 2 + k 2 ⁢ t 2 ) , inverse-Jacobi-elliptic-cn 𝑥 𝑘 superscript subscript 𝑥 1 𝑡 1 superscript 𝑡 2 superscript superscript 𝑘 ′ 2 superscript 𝑘 2 superscript 𝑡 2 {\displaystyle{\displaystyle\operatorname{arccn}\left(x,k\right)=\int_{x}^{1}% \frac{\mathrm{d}t}{\sqrt{(1-t^{2})({k^{\prime}}^{2}+k^{2}t^{2})}},}}
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    DLMF id
    DLMF:22.15.E13
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    constraint
    - 1 ≤ x ≤ 1 1 𝑥 1 {\displaystyle{\displaystyle-1\leq x\leq 1}}
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    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
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