DLMF:16.4.E9 (Q5203)

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DLMF:16.4.E9
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    Statements

    test
    F 4 5 ⁡ ( a , 1 2 ⁢ a + 1 , b , c , d 1 2 ⁢ a , a - b + 1 , a - c + 1 , a - d + 1 ; 1 ) = Γ ⁡ ( a - b + 1 ) ⁢ Γ ⁡ ( a - c + 1 ) ⁢ Γ ⁡ ( a - d + 1 ) ⁢ Γ ⁡ ( a - b - c - d + 1 ) Γ ⁡ ( a + 1 ) ⁢ Γ ⁡ ( a - b - c + 1 ) ⁢ Γ ⁡ ( a - b - d + 1 ) ⁢ Γ ⁡ ( a - c - d + 1 ) , Gauss-hypergeometric-pFq 5 4 𝑎 1 2 𝑎 1 𝑏 𝑐 𝑑 1 2 𝑎 𝑎 𝑏 1 𝑎 𝑐 1 𝑎 𝑑 1 1 Euler-Gamma 𝑎 𝑏 1 Euler-Gamma 𝑎 𝑐 1 Euler-Gamma 𝑎 𝑑 1 Euler-Gamma 𝑎 𝑏 𝑐 𝑑 1 Euler-Gamma 𝑎 1 Euler-Gamma 𝑎 𝑏 𝑐 1 Euler-Gamma 𝑎 𝑏 𝑑 1 Euler-Gamma 𝑎 𝑐 𝑑 1 {\displaystyle{\displaystyle{{}_{5}F_{4}}\left({a,\frac{1}{2}a+1,b,c,d\atop% \frac{1}{2}a,a-b+1,a-c+1,a-d+1};1\right)=\frac{\Gamma\left(a-b+1\right)\Gamma% \left(a-c+1\right)\Gamma\left(a-d+1\right)\Gamma\left(a-b-c-d+1\right)}{\Gamma% \left(a+1\right)\Gamma\left(a-b-c+1\right)\Gamma\left(a-b-d+1\right)\Gamma% \left(a-c-d+1\right)},}}
    0 references
    DLMF id
    DLMF:16.4.E9
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2addec
    0 references
    Q11125
    test
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; z ) Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
    xml-id
    C16.S2.m1afdec
    0 references
    Q11693
    test
    a , a 1 , … , a p 𝑎 subscript 𝑎 1 … subscript 𝑎 𝑝 {\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}
    xml-id
    C16.S1.XMD4.m1gdec
    0 references
    Q11694
    test
    b , b 1 , … , b q 𝑏 subscript 𝑏 1 … subscript 𝑏 𝑞 {\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}
    xml-id
    C16.S1.XMD5.m1fdec
    0 references
     
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