DLMF:35.7.E7 (Q9818)

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DLMF:35.7.E7
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    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)}},}}
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    DLMF id
    DLMF:35.7.E7
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    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)}}
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