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DLMF:19.25.E32 - MaRDI portal

DLMF:19.25.E32 (Q7236)

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DLMF:19.25.E32
No description defined

    Statements

    DLMF defining formula
    arc ⁢ p ⁣ s ⁡ ( x , k ) = R F ⁡ ( x 2 , x 2 + Δ ⁢ ( q , p ) , x 2 + Δ ⁢ ( r , p ) ) , inverse-abstract-Jacobi-elliptic p s 𝑥 𝑘 Carlson-integral-RF superscript 𝑥 2 superscript 𝑥 2 Δ q p superscript 𝑥 2 Δ r p {\displaystyle{\displaystyle\operatorname{arcps}\left(x,k\right)=R_{F}\left(x^% {2},x^{2}+\Delta(\mathrm{q,p}),x^{2}+\Delta(\mathrm{r,p})\right),}}
    0 references
    Symbols used
    symmetric elliptic integral of first kind
    DLMF 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.m2ajdec
    0 references
    real or complex modulus
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1aedec
    0 references
    function (locally)
    DLMF defining formula
    Δ ⁢ ( p , q ) Δ p q {\displaystyle{\displaystyle\Delta(\mathrm{p,q})}}
    xml-id
    C19.S25.XMD2.m1bdec
    0 references

    Identifiers

     
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