DLMF:19.25.E34 (Q6542)

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DLMF:19.25.E34
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    Statements

    Defining formula
    arc ⁢ p ⁣ q ⁡ ( x , k ) = w ⁢ R F ⁡ ( x 2 , 1 , 1 + Δ ⁢ ( r , q ) ⁢ w ) , inverse-abstract-Jacobi-elliptic p q 𝑥 𝑘 𝑤 Carlson-integral-RF superscript 𝑥 2 1 1 Δ r q 𝑤 {\displaystyle{\displaystyle\operatorname{arcpq}\left(x,k\right)=\sqrt{w}R_{F}% \left(x^{2},1,1+\Delta(\mathrm{r,q})w\right),}}
    0 references
    DLMF id
    DLMF:19.25.E34
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    constraint
    w = ( 1 - x 2 ) / Δ ⁢ ( q , p ) 𝑤 1 superscript 𝑥 2 Δ q p {\displaystyle{\displaystyle w=\ifrac{(1-x^{2})}{\Delta(\mathrm{q,p})}}}
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    Symbols used
    symmetric elliptic integral of first kind
    Defining formula
    R F ⁡ ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E1.m2aldec
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    Q11808
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1agdec
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    function (locally)
    Defining formula
    Δ ⁢ ( p , q ) Δ p q {\displaystyle{\displaystyle\Delta(\mathrm{p,q})}}
    xml-id
    C19.S25.XMD2.m1ddec
    0 references
     
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