Power of One plus x in terms of Gaussian Hypergeometric Function

Theorem

 * $\ds {}_2 \map {F_1} {-p, 1; 1; -x} = \paren {1 + x}^p$

where:
 * $x$ and $p$ are real numbers with $\size x < 1$
 * ${}_2 F_1$ denotes the Gaussian hypergeometric function.