DLMF:35.8.E5 (Q9827)

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DLMF:35.8.E5
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    F 2 3 ( a 1 , a 2 , a 3 b 1 , b 2 ; 𝐈 ) = Γ m ( b 2 ) Γ m ( c ) Γ m ( b 2 - a 3 ) Γ m ( c + a 3 ) F 2 3 ( b 1 - a 1 , b 1 - a 2 , a 3 b 1 , c + a 3 ; 𝐈 ) , Gauss-hypergeometric-of-matrix-pFq 3 2 subscript 𝑎 1 subscript 𝑎 2 subscript 𝑎 3 subscript 𝑏 1 subscript 𝑏 2 𝐈 multivariate-Euler-Gamma 𝑚 subscript 𝑏 2 multivariate-Euler-Gamma 𝑚 𝑐 multivariate-Euler-Gamma 𝑚 subscript 𝑏 2 subscript 𝑎 3 multivariate-Euler-Gamma 𝑚 𝑐 subscript 𝑎 3 Gauss-hypergeometric-of-matrix-pFq 3 2 subscript 𝑏 1 subscript 𝑎 1 subscript 𝑏 1 subscript 𝑎 2 subscript 𝑎 3 subscript 𝑏 1 𝑐 subscript 𝑎 3 𝐈 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a_{1},a_{2},a_{3}\atop b_{1},b% _{2}};\mathbf{I}\right)=\frac{\Gamma_{m}\left(b_{2}\right)\Gamma_{m}\left(c% \right)}{\Gamma_{m}\left(b_{2}-a_{3}\right)\Gamma_{m}\left(c+a_{3}\right)}\*{{% }_{3}F_{2}}\left({b_{1}-a_{1},b_{1}-a_{2},a_{3}\atop b_{1},c+a_{3}};\mathbf{I}% \right),}}
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    DLMF:35.8.E5
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