Advertisement

Summation Methods

  • Carlos A. Berenstein
  • Roger Gay

Abstract

Given a power series \( f\left( z \right) = \sum\nolimits_{n \geqslant 0} {{a_n}} {z^n}\) of radius of convergence R, 0 < R < ∞, we are trying to find explicitly the analytic continuation of f to the largest domain, star-shaped with respect to the origin, to which f admits an analytic continuation. Let us denote by D(f) that domain. (Why is it well defined?) We shall obtain D(f) as the union of certain domains B ρ (f),such that in each of them we shall be able to describe explicitly the analytic continuation of f, these domains are parametrized by ρ ≥ 1. The domain D(f) is called the star of holomorphy of f. We start by explaining how to determine B(f) = B1 (f),usually called the Borel polygon of f.

Keywords

Holomorphic Function Entire Function Analytic Continuation Finite Type Exponential Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • Carlos A. Berenstein
    • 1
  • Roger Gay
    • 2
  1. 1.Mathematics Department and Institute for Systems ResearchUniversity of MarylandCollege ParkUSA
  2. 2.Centre de Recherche en MathématiquesUniversité de Bordeaux ITalence (cedex)France

Personalised recommendations