Arcsine Function in terms of Gaussian Hypergeometric Function

Theorem

 * $\arcsin x = x \map F {\dfrac 1 2, \dfrac 1 2; \dfrac 3 2; x^2}$

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

Also presented as
This result can also be seen presented in the form:


 * $\map F {\dfrac 1 2, \dfrac 1 2; \dfrac 3 2; x^2} = \dfrac {\arcsin x} x$