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 ?
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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.)