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Letters in Mathematical Physics

, Volume 13, Issue 4, pp 273–281 | Cite as

Constructive inverse function theorems

  • Hugo H. Torriani
Article

Abstract

An explicit method for finding every coefficient of the reversed series of a power series in one variable is presented. We also show how implicit functions on the plane may be solved for one of the variables. Our approach to the Lagrange inversion formula is based on factorization properties of partitions of integers and distributions of distinguishable objects. These results and techniques may have many applications in numerical analysis, combinatorics, and soliton theory.

AMS subject classifications (1980)

Primary 13F25 secondary 05A17 26A06 26B10 26E05 30B10 32A05 65D05 

Key words and phrases

Inverse function theorem implicit function theorem Lagrange inversion formula partitions of integers distributions of distinguishable objects 

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Copyright information

© D. Reidel Publishing Company 1987

Authors and Affiliations

  • Hugo H. Torriani
    • 1
  1. 1.Instituto de Matemática, Estatística e Ciência da ComputaçãoUniversidade Estadual de CampinasCampinasBrazil

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