power series of inverse trig functions

zeebo17

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!

CompuChip

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 x^1/(2n) is already non-trivial.

g_edgar

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

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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zeebo17	power series of inverse trig functions Tweet 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!

CompuChip Blog Entries: 5 Recognitions: Homework Help Science Advisor	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 x^1/(2n) is already non-trivial.

g_edgar	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	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.