DLMF:35.7.E7 (Q9818)

From DRMF
Revision as of 14:58, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:35.7.E7
No description defined

    Statements

    Defining formula
    F 1 2 ⁡ ( a , b c ; 𝐈 ) = Γ m ⁡ ( c ) ⁢ Γ m ⁡ ( c - a - b ) Γ m ⁡ ( c - a ) ⁢ Γ m ⁡ ( c - b ) , Gauss-hypergeometric-of-matrix-pFq 2 1 𝑎 𝑏 𝑐 𝐈 multivariate-Euler-Gamma 𝑚 𝑐 multivariate-Euler-Gamma 𝑚 𝑐 𝑎 𝑏 multivariate-Euler-Gamma 𝑚 𝑐 𝑎 multivariate-Euler-Gamma 𝑚 𝑐 𝑏 {\displaystyle{\displaystyle{{{}_{2}F_{1}}\left({a,b\atop c};\mathbf{I}\right)% =\frac{\Gamma_{m}\left(c\right)\Gamma_{m}\left(c-a-b\right)}{\Gamma_{m}\left(c% -a\right)\Gamma_{m}\left(c-b\right)}},}}
    0 references
    DLMF id
    DLMF:35.7.E7
    0 references
    constraint
    ℜ ⁡ ( c ) , ℜ ⁡ ( c - a - b ) > 1 2 ⁢ ( m - 1 ) 𝑐 𝑐 𝑎 𝑏 1 2 𝑚 1 {\displaystyle{\displaystyle\Re(c),\Re(c-a-b)>\frac{1}{2}(m-1)}}
    0 references
    Symbols used
    generalized hypergeometric function of matrix argument
    Defining formula
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; 𝐓 ) Gauss-hypergeometric-of-matrix-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝐓 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{\mathbf{T}}\right)}}
    xml-id
    C35.S8.E1.m2afdec
    0 references
    Q12725
    Defining formula
    Γ m ⁡ ( a ) multivariate-Euler-Gamma 𝑚 𝑎 {\displaystyle{\displaystyle\Gamma_{\NVar{m}}\left(\NVar{a}\right)}}
    xml-id
    C35.S3.SS1.m1aadec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
    0 references
    Q12726
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C35.S1.XMD1.m1edec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q9818&oldid=52848"