A ridiculously simple and explicit implicit function theorem

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.

References in corpus (1)

• Some variants of the exponential formula, with application to the multivariate Tutte polynomial (alias Potts model)

Cited by in corpus (6)

• Lagrange Inversion
• The leading root of the partial theta function
• The virtual K-theory of Quot schemes of surfaces
• Lagrange Inversion Formula by Induction
• The Combinatorics of Higher Derivatives of Implicit Functions
• Graph rules for the linked cluster expansion of the Legendre effective action