# Power series of inverse trig functions

1. ### zeebo17

41
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!

2. ### CompuChip

4,299
I don't think so.
Even for the simplest of functions you already run into trouble, consider for example y = x2n (for n = 1, 2, ...). The power series for x1/(2n) is already non-trivial.

3. ### g_edgar

607
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.

4. ### MichaelMi

3
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.