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International Journal of Mathematics and Mathematical Sciences
Volume 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 Hindawi Publishing Corporation. 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 N terms of the series. We show several examples of its application in calculating the inverses of some special functions.