International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 58, Pages 3699-3715
Nested derivatives: a simple method for computing series expansions of inverse functions
Department of Mathematics, State University of New York at New Paltz, New Paltz 12561–2443, NY, USA
Received 28 March 2003
Copyright © 2003 Diego Dominici. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We give an algorithm to compute the series expansion for the
inverse of a given function. The algorithm is extremely easy to
implement and gives the first terms of the series. We show
several examples of its application in calculating the inverses
of some special functions.