Resummation of formal series. Solutions of second order linear complex ordinary differential equations near irregular singularities

DOI10.1007/BF01385638zbMath0701.30002OpenAlexW38828115MaRDI QIDQ913976

Jean Thomann

Publication date: 1991

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133514

zbMATH Keywords

singularitiesBorel-Padé-type approximants

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Power series (including lacunary series) in one complex variable (30B10) Numerical investigation of stability of solutions to ordinary differential equations (65L07) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Asymptotic properties of solutions to ordinary differential equations (34D05) Numerical summation of series (65B10) Asymptotic representations in the complex plane (30E15) Boundary behavior of power series in one complex variable; over-convergence (30B30) Analytic continuation of functions of one complex variable (30B40)

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Comparison between Borel-Padé summation and factorial series, as time integration methods, Stokes phenomenon for the prolate spheroidal wave equation, Summation of divergent power series by means of factorial series, Time integration algorithm based on divergent series resummation, for ordinary and partial differential equations, Exact semiclassical expansions for one-dimensional quantum oscillators, Divergence and summability of normal forms of systems of differential equations with nilpotent linear part, Unnamed Item, An algorithm of multisummation of formal power series, solutions of linear ODEs.

Cites Work

• Padé-type approximation and general orthogonal polynomials
• On the convergence of Padé-type approximants to analytic functions
• Placement of cuts in Padé-like approximation
• Rational approximation to formal power series
• Asymptotics for orthogonal polynomials
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