Arcsine Function in terms of Gaussian Hypergeometric Function

Theorem

 * $\displaystyle \arcsin x = x \, {}_2 \map {F_1} {\frac 1 2, \frac 1 2; \frac 3 2; x^2}$

where:
 * $x$ is a real number with $\size x \le 1$
 * $\arcsin$ denotes the arcsine function
 * ${}_2 F_1$ denotes the Gaussian hypergeometric function.