Constructive inverse function theorems
type: Item
instance of: scholarly article
title: Constructive inverse function theorems
zbMATH Open document ID: 0623.30004
DOI: 10.1007/BF00401155
published in: Letters in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 30B10
Mathematics Subject Classification ID: 32A05
zbMATH DE Number: 4010850
zbMATH Keywords: implicit functions
zbMATH Keywords: Lagrange inversion formula
zbMATH Keywords: partitions of integers
author: Hugo H. Torriani
MaRDI profile type: Publication
cites work: On the mathematical foundations of electrical circuit theory
cites work: Dual operators and Lagrange inversion in several variables
cites work: ON AN APPLICATION OF THE MULTIPLE LOGARITHMIC RESIDUE TO THE EXPANSION OF IMPLICIT FUNCTIONS IN POWER SERIES
cites work: Integral powers of the Sturm-Liouville operator and the theory of partitions
cites work: Constructive implicit function theorems
cites work: Kac-Moody Lie algebras and soliton equations. II: Lax equations associated with \(A_ 1^{(1)}\)
cites work: Complete integrability of the Kadomtsev-Petviashvili equation
cites work: Korteweg-deVries Equation and Generalizations. V. Uniqueness and Nonexistence of Polynomial Conservation Laws
full work available at URL: https://doi.org/10.1007/bf00401155
OpenAlex ID: W2089476476
description: scientific article; zbMATH DE number 4010850