DLMF:19.26.E22 (Q7275)

From MaRDI portal
No description defined
Language Label Description Also known as
English
DLMF:19.26.E22
No description defined

    Statements

    DLMF defining formula
    R J ⁡ ( x , y , z , p ) = 2 ⁢ R J ⁡ ( x + λ , y + λ , z + λ , p + λ ) + 3 ⁢ R C ⁡ ( α 2 , β 2 ) , Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 2 Carlson-integral-RJ 𝑥 𝜆 𝑦 𝜆 𝑧 𝜆 𝑝 𝜆 3 Carlson-integral-RC superscript 𝛼 2 superscript 𝛽 2 {\displaystyle{\displaystyle R_{J}\left(x,y,z,p\right)=2R_{J}\left(x+\lambda,y% +\lambda,z+\lambda,p+\lambda\right)+3R_{C}\left(\alpha^{2},\beta^{2}\right),}}
    0 references
    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    DLMF defining formula
    R C ⁡ ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    xml-id
    C19.S2.E17.m2aedec
    0 references
    symmetric elliptic integral of third kind
    DLMF defining formula
    R J ⁡ ( x , y , z , p ) Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 {\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}% \right)}}
    xml-id
    C19.S16.E2.m2aadec
    0 references
    positive
    DLMF defining formula
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    xml-id
    C19.S26.XMD1.m1pdec
    0 references
    α
    DLMF defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C19.S26.XMD11.m1dec
    0 references
    β
    DLMF defining formula
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C19.S26.XMD12.m1dec
    0 references
    positive
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C19.S26.XMD2.m1qdec
    0 references
    positive
    DLMF defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C19.S26.XMD3.m1rdec
    0 references
    positive
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C19.S26.XMD4.m1odec
    0 references

    Identifiers

     
    Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Item:Q7275&oldid=24175709"
    Powered by MediaWiki