DLMF:16.4.E15 (Q5209)

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DLMF:16.4.E15
No description defined

    Statements

    Defining formula
    F 6 7 ⁡ ( a , 1 2 ⁢ a + 1 , b , c , d , e , f 1 2 ⁢ a , a - b + 1 , a - c + 1 , a - d + 1 , a - e + 1 , a - f + 1 ; 1 ) = Γ ⁡ ( a - d + 1 ) ⁢ Γ ⁡ ( a - e + 1 ) ⁢ Γ ⁡ ( a - f + 1 ) ⁢ Γ ⁡ ( a - d - e - f + 1 ) Γ ⁡ ( a + 1 ) ⁢ Γ ⁡ ( a - d - e + 1 ) ⁢ Γ ⁡ ( a - d - f + 1 ) ⁢ Γ ⁡ ( a - e - f + 1 ) ⁢ F 3 4 ⁡ ( a - b - c + 1 , d , e , f a - b + 1 , a - c + 1 , d + e + f - a ; 1 ) , Gauss-hypergeometric-pFq 7 6 𝑎 1 2 𝑎 1 𝑏 𝑐 𝑑 𝑒 𝑓 1 2 𝑎 𝑎 𝑏 1 𝑎 𝑐 1 𝑎 𝑑 1 𝑎 𝑒 1 𝑎 𝑓 1 1 Euler-Gamma 𝑎 𝑑 1 Euler-Gamma 𝑎 𝑒 1 Euler-Gamma 𝑎 𝑓 1 Euler-Gamma 𝑎 𝑑 𝑒 𝑓 1 Euler-Gamma 𝑎 1 Euler-Gamma 𝑎 𝑑 𝑒 1 Euler-Gamma 𝑎 𝑑 𝑓 1 Euler-Gamma 𝑎 𝑒 𝑓 1 Gauss-hypergeometric-pFq 4 3 𝑎 𝑏 𝑐 1 𝑑 𝑒 𝑓 𝑎 𝑏 1 𝑎 𝑐 1 𝑑 𝑒 𝑓 𝑎 1 {\displaystyle{\displaystyle{{}_{7}F_{6}}\left({a,\frac{1}{2}a+1,b,c,d,e,f% \atop\frac{1}{2}a,a-b+1,a-c+1,a-d+1,a-e+1,a-f+1};1\right)=\frac{\Gamma\left(a-% d+1\right)\Gamma\left(a-e+1\right)\Gamma\left(a-f+1\right)\Gamma\left(a-d-e-f+% 1\right)}{\Gamma\left(a+1\right)\Gamma\left(a-d-e+1\right)\Gamma\left(a-d-f+1% \right)\Gamma\left(a-e-f+1\right)}{{}_{4}F_{3}}\left({a-b-c+1,d,e,f\atop a-b+1% ,a-c+1,d+e+f-a};1\right),}}
    0 references
    DLMF id
    DLMF:16.4.E15
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2afdec
    0 references
    Q11125
    Defining formula
    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.m1aldec
    0 references
    Q11695
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C16.S4.XMD1.m1ddec
    0 references
    Q11696
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C16.S4.XMD2.m1ddec
    0 references
    Q11697
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C16.S4.XMD3.m1ddec
    0 references
    Q11698
    Defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C16.S4.XMD4.m1ddec
    0 references
    Q11699
    Defining formula
    e 𝑒 {\displaystyle{\displaystyle e}}
    xml-id
    C16.S4.XMD5.m1ddec
    0 references
     
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