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),}}
    0 references
    DLMF id
    DLMF:16.4.E11
    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.m2aedec
    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.m1ahdec
    0 references
    Q11695
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C16.S4.XMD1.m1dec
    0 references
    Q11696
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C16.S4.XMD2.m1dec
    0 references
    Q11697
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C16.S4.XMD3.m1dec
    0 references
    Q11698
    Defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C16.S4.XMD4.m1dec
    0 references
    Q11699
    Defining formula
    e 𝑒 {\displaystyle{\displaystyle e}}
    xml-id
    C16.S4.XMD5.m1dec
    0 references
     
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