DLMF:16.4.E4 (Q5198)

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DLMF:16.4.E4
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    Defining formula
    F 2 3 ⁡ ( a , b , c a - b + 1 , a - c + 1 ; 1 ) = Γ ⁡ ( 1 2 ⁢ a + 1 ) ⁢ Γ ⁡ ( a - b + 1 ) ⁢ Γ ⁡ ( a - c + 1 ) ⁢ Γ ⁡ ( 1 2 ⁢ a - b - c + 1 ) Γ ⁡ ( a + 1 ) ⁢ Γ ⁡ ( 1 2 ⁢ a - b + 1 ) ⁢ Γ ⁡ ( 1 2 ⁢ a - c + 1 ) ⁢ Γ ⁡ ( a - b - c + 1 ) , Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑎 𝑏 1 𝑎 𝑐 1 1 Euler-Gamma 1 2 𝑎 1 Euler-Gamma 𝑎 𝑏 1 Euler-Gamma 𝑎 𝑐 1 Euler-Gamma 1 2 𝑎 𝑏 𝑐 1 Euler-Gamma 𝑎 1 Euler-Gamma 1 2 𝑎 𝑏 1 Euler-Gamma 1 2 𝑎 𝑐 1 Euler-Gamma 𝑎 𝑏 𝑐 1 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a,b,c\atop a-b+1,a-c+1};1% \right)=\frac{\Gamma\left(\frac{1}{2}a+1\right)\Gamma\left(a-b+1\right)\Gamma% \left(a-c+1\right)\Gamma\left(\frac{1}{2}a-b-c+1\right)}{\Gamma\left(a+1\right% )\Gamma\left(\frac{1}{2}a-b+1\right)\Gamma\left(\frac{1}{2}a-c+1\right)\Gamma% \left(a-b-c+1\right)},}}
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    DLMF id
    DLMF:16.4.E4
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