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Power series of inverse trig functions 
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#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

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P: 4,300

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: 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 [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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