
#1
Nov1209, 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! 



#2
Nov1309, 07:41 AM

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 = x^{2n} (for n = 1, 2, ...). The power series for x^{1/(2n)} is already nontrivial. 



#3
Nov1309, 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] (1x^2)^{1/2}[/itex] and integrate termbyterm. 



#4
Nov1609, 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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