A ridiculously simple and explicit implicit function theorem

Details A ridiculously simple and explicit implicit function theorem A ridiculously simple and explicit implicit function theorem

2009-01-31

arxiv.org/abs/0902.0069v1

Seminaire Lotharingien de Combinatoire 61A, article 61Ad (2009)

Mathematics

Complex Variables

Scientific paper

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.

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