DLMF:35.7.E8 (Q9819): Difference between revisions

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DLMF:35.7.E8
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    Statements

    Defining formula
    F 1 2 ⁡ ( a , b c ; 𝐓 ) = Γ m ⁡ ( c ) ⁢ Γ m ⁡ ( c - a - b ) Γ m ⁡ ( c - a ) ⁢ Γ m ⁡ ( c - b ) ⁢ F 1 2 ⁡ ( a , b a + b - c + 1 2 ⁢ ( m + 1 ) ; 𝐈 - 𝐓 ) , Gauss-hypergeometric-of-matrix-pFq 2 1 𝑎 𝑏 𝑐 𝐓 multivariate-Euler-Gamma 𝑚 𝑐 multivariate-Euler-Gamma 𝑚 𝑐 𝑎 𝑏 multivariate-Euler-Gamma 𝑚 𝑐 𝑎 multivariate-Euler-Gamma 𝑚 𝑐 𝑏 Gauss-hypergeometric-of-matrix-pFq 2 1 𝑎 𝑏 𝑎 𝑏 𝑐 1 2 𝑚 1 𝐈 𝐓 {\displaystyle{\displaystyle{{{}_{2}F_{1}}\left({a,b\atop c};\mathbf{T}\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)}}\*{{}_{2}F_{1}}\left({a,b\atop a+b-c+% \frac{1}{2}(m+1)};\mathbf{I}-\mathbf{T}\right),}}
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    DLMF id
    DLMF:35.7.E8
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