# How to compute the following taylor series expansion

I'm supposed to find the Taylor series expansion of $(\arcsin(x))^2$, but I can't think of a proper solution .The derivative doesn't show much promise since it still contains the $\arcsin(x)$ function.

Any hints ?

• And that would give me the expansion of $arcsin(x)$, right? Well I'm trying to get the expansion of the squared function, I don't think it's that easy squaring an infinite series, this is the main purpose of this exercise.. – giova Nov 19 '14 at 23:24

As the power series of $arcsin$ is absolutely convergent for $|x| <1$, you can simply take the Cauchy product of the power series. (Check on a textbook that describes multiplication of two power series.)