DLMF:22.15.E22 (Q7117)

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DLMF:22.15.E22
No description defined

    Statements

    Defining formula
    arcds ⁡ ( x , k ) = ∫ x ∞ d t ( t 2 + k 2 ) ⁢ ( t 2 - k ′ 2 ) , inverse-Jacobi-elliptic-ds 𝑥 𝑘 superscript subscript 𝑥 𝑡 superscript 𝑡 2 superscript 𝑘 2 superscript 𝑡 2 superscript superscript 𝑘 ′ 2 {\displaystyle{\displaystyle\operatorname{arcds}\left(x,k\right)=\int_{x}^{% \infty}\frac{\mathrm{d}t}{\sqrt{(t^{2}+k^{2})(t^{2}-{k^{\prime}}^{2})}},}}
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    DLMF id
    DLMF:22.15.E22
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    constraint
    k ′ ≤ x < ∞ superscript 𝑘 ′ 𝑥 {\displaystyle{\displaystyle k^{\prime}\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.m1akdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3akdec
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    Q12018
    Defining formula
    arcds ⁡ ( x , k ) inverse-Jacobi-elliptic-ds 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arcds}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S15.SS1.p1.m10adec
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    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1udec
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    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1udec
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    Q11988
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1gdec
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