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arxiv: 0902.0069 · v1 · submitted 2009-01-31 · 🧮 math.CV · math.CO

A ridiculously simple and explicit implicit function theorem

classification 🧮 math.CV math.CO
keywords explicitformulaproblemseriesanalyticcomplexfixed-pointformal
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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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