Nested Derivatives: A simple method for computing series expansions of inverse functions

TL;DR

This paper introduces a straightforward algorithm for computing series expansions of inverse functions, demonstrating its simplicity and effectiveness through various examples involving special functions.

Contribution

The paper presents a novel, easy-to-implement algorithm for calculating series expansions of inverse functions, with practical applications shown through multiple examples.

Findings

Efficient computation of inverse function series expansions.

Algorithm is simple to implement and yields the first N terms.

Successful application to special functions.

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.