Dougall's Hypergeometric Theorem/Corollary 2

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

Then:


 * $\ds \map { {}_4 \operatorname F_3} { { {\dfrac n 2 + 1, -x, -y, 1} \atop {\dfrac n 2, x + n + 1, y + n + 1} } \, \middle \vert \, 1} = \dfrac {\paren {x + n} \paren {y + n} } {n \paren {x + y + n} } $

Proof
Set $z = -1$ in Dougall's Hypergeometric Theorem

Before substitution:

After substitution: