DLMF:16.4.E11 (Q5205)

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DLMF:16.4.E11
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    Statements

    Defining formula
    F 2 3 ⁡ ( a , b , c d , e ; 1 ) = Γ ⁡ ( e ) ⁢ Γ ⁡ ( d + e - a - b - c ) Γ ⁡ ( e - a ) ⁢ Γ ⁡ ( d + e - b - c ) ⁢ F 2 3 ⁡ ( a , d - b , d - c d , d + e - b - c ; 1 ) , Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑑 𝑒 1 Euler-Gamma 𝑒 Euler-Gamma 𝑑 𝑒 𝑎 𝑏 𝑐 Euler-Gamma 𝑒 𝑎 Euler-Gamma 𝑑 𝑒 𝑏 𝑐 Gauss-hypergeometric-pFq 3 2 𝑎 𝑑 𝑏 𝑑 𝑐 𝑑 𝑑 𝑒 𝑏 𝑐 1 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a,b,c\atop d,e};1\right)=\frac% {\Gamma\left(e\right)\Gamma\left(d+e-a-b-c\right)}{\Gamma\left(e-a\right)% \Gamma\left(d+e-b-c\right)}{{}_{3}F_{2}}\left({a,d-b,d-c\atop d,d+e-b-c};1% \right),}}
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    DLMF id
    DLMF:16.4.E11
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