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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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    $\begingroup$ 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.. $\endgroup$ – giova Nov 19 '14 at 23:24
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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.)

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