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A ridiculously simple and explicit implicit function theorem

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arxiv 0902.0069 v1 pith:JZ7G4GPQ submitted 2009-01-31 math.CV math.CO

Alan D. Sokal This is my paper · ORCID
classification math.CVmath.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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Closure under factorization from a result of Furstenberg

    cs.CC 2025-06 accept novelty 7.0 of 10

    Factors of polynomials computed by small constant-depth circuits or formulas are themselves computable by small constant-depth circuits or formulas in characteristic zero and large positive characteristic.

  2. Surface sums in two-dimensional large-$N$ lattice Yang--Mills: Cancellations and explicit computations for general loops

    math.PR 2025-08 unverdicted novelty 6.0 of 10

    A peeling algorithm exposes cancellations in 2D large-N lattice Yang-Mills surface sums, yielding new explicit Wilson loop formulas and spectral measure convergence.

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