Formula:KLS:01.07:06

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\HyperpFq ⁢ 43 ⁢ @ ⁢ @ - n , a , b , c ⁢ d , e , f ⁢ 1 = ( e - a ) n ⁢ ( f - a ) n ( e ) n ⁢ ( f ) n ⁢ \HyperpFq ⁢ 43 ⁢ @ ⁢ @ - n , a , d - b , d - c ⁢ d , a - e - n + 1 , a - f - n + 11 formulae-sequence \HyperpFq 43 @ @ 𝑛 𝑎 𝑏 𝑐 𝑑 𝑒 𝑓 1 Pochhammer-symbol 𝑒 𝑎 𝑛 Pochhammer-symbol 𝑓 𝑎 𝑛 Pochhammer-symbol 𝑒 𝑛 Pochhammer-symbol 𝑓 𝑛 \HyperpFq 43 @ @ 𝑛 𝑎 𝑑 𝑏 𝑑 𝑐 𝑑 𝑎 𝑒 𝑛 1 𝑎 𝑓 𝑛 11 {\displaystyle{\displaystyle{\displaystyle{}{}\HyperpFq{4}{3}@@{-n,a,b,c}{d,e,% f}{1}{}=\frac{{\left(e-a\right)_{n}}{\left(f-a\right)_{n}}}{{\left(e\right)_{n% }}{\left(f\right)_{n}}}\HyperpFq{4}{3}@@{-n,a,d-b,d-c}{d,a-e-n+1,a-f-n+1}{1}}}}

Proof

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Symbols List

F q p subscript subscript 𝐹 𝑞 𝑝 {\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}  : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1
( a ) n subscript 𝑎 𝑛 {\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

Bibliography

Equation in Section 1.7 of KLS.

URL links

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