Power series of inverse trig functions

  1. 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. jcsd
  3. CompuChip

    CompuChip 4,297
    Science Advisor
    Homework Helper

    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.
     
  4. 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.
     
  5. 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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