DLMF:22.15.E21 (Q7116)

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DLMF:22.15.E21
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    Statements

    Defining formula
    arcns ⁡ ( x , k ) = ∫ x ∞ d t ( t 2 - 1 ) ⁢ ( t 2 - k 2 ) , inverse-Jacobi-elliptic-ns 𝑥 𝑘 superscript subscript 𝑥 𝑡 superscript 𝑡 2 1 superscript 𝑡 2 superscript 𝑘 2 {\displaystyle{\displaystyle\operatorname{arcns}\left(x,k\right)=\int_{x}^{% \infty}\frac{\mathrm{d}t}{\sqrt{(t^{2}-1)(t^{2}-k^{2})}},}}
    0 references
    DLMF id
    DLMF:22.15.E21
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    constraint
    1 ≤ x < ∞ 1 𝑥 {\displaystyle{\displaystyle 1\leq x<\infty}}
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    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ajdec
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    Q12017
    Defining formula
    arcns ⁡ ( x , k ) inverse-Jacobi-elliptic-ns 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arcns}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S15.SS1.p1.m7adec
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    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1tdec
    0 references
     
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