Resummation of formal series. Solutions of second order linear complex ordinary differential equations near irregular singularities
type: Item
instance of: scholarly article
title: Resummation of formal series. Solutions of second order linear complex ordinary differential equations near irregular singularities
zbMATH Open document ID: 0701.30002
DOI: 10.1007/BF01385638
author: Jean Thomann
published in: Numerische Mathematik
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133514
review text: Formulae for solutions of complex ordinary differential equations in the neighbourhood of irregular singularities contain almost every time divergent series. The \(k\)-summation theory developed in the field of analytic functional equations by J. P. Ramis provides us with a tool to perform in different ways some effective calculations and to compare their results. In the case of second order differential equations, we can compute the sum of the divergent series by Borel-Padé-type approximants with orthogonal Legendre or Chebyshev generating polynomials or direct Padé-type approximants with Laguerre generating polynomials, which are a generalization of classical factorial series. We take full advantage of the possibilities of computer algebra, especially of exact rational evaluation.
Mathematics Subject Classification ID: 30B10
Mathematics Subject Classification ID: 30B30
Mathematics Subject Classification ID: 30B40
Mathematics Subject Classification ID: 30E15
Mathematics Subject Classification ID: 34M35
Mathematics Subject Classification ID: 40A05
Mathematics Subject Classification ID: 65B10
Mathematics Subject Classification ID: 65L07
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 4148469
zbMATH Keywords: singularities
zbMATH Keywords: Borel-Padé-type approximants
MaRDI profile type: Publication
cites work: Placement of cuts in Padé-like approximation
cites work: Rational approximation to formal power series
cites work: Padé-type approximation and general orthogonal polynomials
cites work: On the convergence of Padé-type approximants to analytic functions
cites work: Q3209217
cites work: Q4649619
cites work: Q4747449
cites work: Q3264312
cites work: Asymptotics for orthogonal polynomials
cites work: Q3339159
cites work: Q4148241
OpenAlex ID: W38828115
Recommended article: Resurgence-summability of ramified formal series depending of a parameter and solutions of linear differential equations
Recommended article: Resurgence of formal series solutions of nonlinear differential and difference equations
Recommended article: Q5445979
Recommended article: Q4467066
Recommended article: Q4009102
Recommended article: Q3606300
Recommended article: On the summability of the formal solutions for some PDEs with irregular singularity
Recommended article: Q3224248
Recommended article: Q3488416
description: scientific article; zbMATH DE number 4148469