Reciprocal of One minus x in terms of Gaussian Hypergeometric Function

Theorem

 * $\dfrac 1 {1 - x} = {}_2 \map {F_1} {1, p; p; x}$

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