International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 58, Pages 3699-3715
doi:10.1155/S0161171203303291

Nested derivatives: a simple method for computing series expansions of inverse functions

Diego Dominici

Department of Mathematics, State University of New York at New Paltz, New Paltz 12561–2443, NY, USA

Received 28 March 2003

Abstract

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 N terms of the series. We show several examples of its application in calculating the inverses of some special functions.