## power series of inverse trig functions

How do you find the power series for inverse trig functions? Can I find the power series for arcsin by manipulating the power series for sin?

Thanks!
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 You can, it is called "reversion" of a series. But the formulas get more and more complicated as you proceed. For arcsin, a better way to find the series is to start with the binomial series for $(1-x^2)^{-1/2}$ and integrate term-by-term.

## power series of inverse trig functions

Identify the inverse trig function as a hypergeometric function, and manipulate the series expansion of the hypergeometric function. Any book on hypergeometric functions will give the necessary formulae.