# power series of inverse trig functions

by zeebo17
Tags: functions, inverse, power, series, trig
 P: 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!
 Sci Advisor HW Helper P: 4,301 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.
 P: 608 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.
P: 3

## 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.

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