Dougall's Hypergeometric Theorem/Corollary 5

Corollary to Dougall's Hypergeometric Theorem
Let $\map \Re {n} < \dfrac 1 2$.

Then:


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

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

Before substitution:

After substitution: