DLMF:22.15.E14 (Q7109)

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DLMF:22.15.E14
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    Statements

    Defining formula
    arcdn ⁡ ( x , k ) = ∫ x 1 d t ( 1 - t 2 ) ⁢ ( t 2 - k ′ 2 ) , inverse-Jacobi-elliptic-dn 𝑥 𝑘 superscript subscript 𝑥 1 𝑡 1 superscript 𝑡 2 superscript 𝑡 2 superscript superscript 𝑘 ′ 2 {\displaystyle{\displaystyle\operatorname{arcdn}\left(x,k\right)=\int_{x}^{1}% \frac{\mathrm{d}t}{\sqrt{(1-t^{2})(t^{2}-{k^{\prime}}^{2})}},}}
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    DLMF id
    DLMF:22.15.E14
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    constraint
    k ′ ≤ x ≤ 1 superscript 𝑘 ′ 𝑥 1 {\displaystyle{\displaystyle k^{\prime}\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.m1acdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
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    Q12009
    Defining formula
    arcdn ⁡ ( x , k ) inverse-Jacobi-elliptic-dn 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arcdn}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S15.SS1.p1.m3acdec
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    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1mdec
    0 references
     
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