Dougall's Hypergeometric Theorem/Corollary 4

Corollary to Dougall's Hypergeometric Theorem
Let $\map \Re {x - n + 1} > 0$.

Then:


 * $\ds \map { {}_5 \operatorname F_4} { { {\dfrac n 2 + 1, n, n, n, -x} \atop {\dfrac n 2, x + n + 1, 1, 1} } \, \middle \vert \, 1} = \dfrac {\map \sin {\pi n} \map \Gamma {x + n + 1} \map \Gamma {x - n + 1} } {\pi n \paren {\map \Gamma {x + 1} }^2 } $

Proof
Set $y = z = -n$ in Dougall's Hypergeometric Theorem

Before substitution:

After substitution: