A ridiculously simple and explicit implicit function theorem
Complex Variables
2009-11-16 v1 Combinatorics
Abstract
I show that the general implicit-function problem (or parametrized fixed-point problem) in one complex variable has an explicit series solution given by a trivial generalization of the Lagrange inversion formula. I give versions of this formula for both analytic functions and formal power series.
Cite
@article{arxiv.0902.0069,
title = {A ridiculously simple and explicit implicit function theorem},
author = {Alan D. Sokal},
journal= {arXiv preprint arXiv:0902.0069},
year = {2009}
}