DLMF:16.4.E14 (Q5208)

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DLMF:16.4.E14
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    Statements

    F 3 4 ( - n , a , b , c d , e , f ; 1 ) = ( e - a ) n ( f - a ) n ( e ) n ( f ) n F 3 4 ( - n , a , d - b , d - c d , a - e - n + 1 , a - f - n + 1 ; 1 ) , Gauss-hypergeometric-pFq 4 3 𝑛 𝑎 𝑏 𝑐 𝑑 𝑒 𝑓 1 Pochhammer 𝑒 𝑎 𝑛 Pochhammer 𝑓 𝑎 𝑛 Pochhammer 𝑒 𝑛 Pochhammer 𝑓 𝑛 Gauss-hypergeometric-pFq 4 3 𝑛 𝑎 𝑑 𝑏 𝑑 𝑐 𝑑 𝑎 𝑒 𝑛 1 𝑎 𝑓 𝑛 1 1 {\displaystyle{\displaystyle{{}_{4}F_{3}}\left({-n,a,b,c\atop d,e,f};1\right)=% \frac{{\left(e-a\right)_{n}}{\left(f-a\right)_{n}}}{{\left(e\right)_{n}}{\left% (f\right)_{n}}}{{}_{4}F_{3}}\left({-n,a,d-b,d-c\atop d,a-e-n+1,a-f-n+1};1% \right),}}
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    DLMF:16.4.E14
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    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)}}
    C16.S2.m1akdec
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    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    C5.S2.SS3.m1acdec
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    a 𝑎 {\displaystyle{\displaystyle a}}
    C16.S4.XMD1.m1cdec
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    b 𝑏 {\displaystyle{\displaystyle b}}
    C16.S4.XMD2.m1cdec
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    c 𝑐 {\displaystyle{\displaystyle c}}
    C16.S4.XMD3.m1cdec
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