Arctangent Function in terms of Gaussian Hypergeometric Function

Theorem

 * $\ds \arctan x = x \, {}_2 \map {F_1} {\frac 1 2, 1; \frac 3 2; -x^2}$

where:
 * $x$ is a real number with $\size x < 1$
 * $\arctan$ denotes the arctangent function
 * ${}_2 F_1$ denotes the Gaussian hypergeometric function.