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DLMF:19.25.E33 - MaRDI portal

DLMF:19.25.E33 (Q7237)

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DLMF:19.25.E33
No description defined

    Statements

    DLMF defining formula
    arc ⁢ s ⁣ p ⁡ ( x , k ) = x ⁢ R F ⁡ ( 1 , 1 + Δ ⁢ ( q , p ) ⁢ x 2 , 1 + Δ ⁢ ( r , p ) ⁢ x 2 ) , inverse-abstract-Jacobi-elliptic s p 𝑥 𝑘 𝑥 Carlson-integral-RF 1 1 Δ q p superscript 𝑥 2 1 Δ r p superscript 𝑥 2 {\displaystyle{\displaystyle\operatorname{arcsp}\left(x,k\right)=xR_{F}\left(1% ,1+\Delta(\mathrm{q,p})x^{2},1+\Delta(\mathrm{r,p})x^{2}\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.m2akdec
    0 references
    real or complex modulus
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1afdec
    0 references
    function (locally)
    DLMF defining formula
    Δ ⁢ ( p , q ) Δ p q {\displaystyle{\displaystyle\Delta(\mathrm{p,q})}}
    xml-id
    C19.S25.XMD2.m1cdec
    0 references

    Identifiers

     
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