power series of inverse trig functions


by zeebo17
Tags: functions, inverse, power, series, trig
zeebo17
zeebo17 is offline
#1
Nov12-09, 10:31 PM
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!
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CompuChip
CompuChip is offline
#2
Nov13-09, 07:41 AM
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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.
g_edgar
g_edgar is offline
#3
Nov13-09, 09:04 AM
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 [itex] (1-x^2)^{-1/2}[/itex] and integrate term-by-term.

MichaelMi
MichaelMi is offline
#4
Nov16-09, 07:37 PM
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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