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Séminaire Lotharingien de Combinatoire, B61Ad (2009), 21 pp.

# Alan D. Sokal

# 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.

Received: January 31, 2009.
Accepted: July 14, 2009.
Final Version: July 15, 2009.

The following versions are available: