DLMF:16.4.E3 (Q5197)

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DLMF:16.4.E3
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    Statements

    Defining formula
    F 2 3 ⁡ ( - n , a , b c , d ; 1 ) = ( c - a ) n ⁢ ( c - b ) n ( c ) n ⁢ ( c - a - b ) n , Gauss-hypergeometric-pFq 3 2 𝑛 𝑎 𝑏 𝑐 𝑑 1 Pochhammer 𝑐 𝑎 𝑛 Pochhammer 𝑐 𝑏 𝑛 Pochhammer 𝑐 𝑛 Pochhammer 𝑐 𝑎 𝑏 𝑛 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({-n,a,b\atop c,d};1\right)=% \frac{{\left(c-a\right)_{n}}{\left(c-b\right)_{n}}}{{\left(c\right)_{n}}{\left% (c-a-b\right)_{n}}},}}
    0 references
    DLMF id
    DLMF:16.4.E3
    0 references
    Symbols used
    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.m1adec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    Q11693
    Defining formula
    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.m1bdec
    0 references
    Q11694
    Defining formula
    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.m1bdec
    0 references
     
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