# Can you find Roots With The Power Series Inverse?

1. Aug 4, 2009

### John Creighto

The following link outlines a method to find the inverse of a power series. I was wondering what would happen if you try this on a polynomial. Since polynomials aren't one to one, I presume that it wouldn't give you all the roots, but might it give you the nearst root. Or will this technique not work on this type of function?

http://www.mathpages.com/home/kmath625/kmath625.htm

Edit: Looking further at the solution, to find the coefficients you have to be able to find the roots. Therefor we could only find at most say around the first five coefficients in general without using numeric techniques.

Edit 2: Although maybe it is better to find the derivative of the inverse more directly, then suggested in the above link. For instance we could chose some point, where we know the inverse, and then use the functions for the derivative of the inverse as outlined here:
http://en.wikipedia.org/wiki/Inverse_functions_and_differentiation#Higher_derivatives

Last edited: Aug 4, 2009