Regularization of certain divergent series of polynomials
Liviu I. Nicolaescu

TL;DR
This paper explores methods to assign meaningful sums to divergent polynomial series using Cesaro and Abel summation techniques, focusing on series involving translation-invariant operators.
Contribution
It introduces a framework for regularizing divergent polynomial series through Cesaro and Abel sums, extending the understanding of such series in analysis.
Findings
Cesaro and Abel sums provide finite values for certain divergent polynomial series.
The study characterizes conditions under which these sums exist and are well-defined.
Applications to translation-invariant operators on polynomial spaces are demonstrated.
Abstract
We investigate the Cesaro and Abel sums of divergent series of the form , where is a real polynomial and is a translation invariant operator on the space of real polynomials.
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Taxonomy
TopicsMathematical functions and polynomials · Meromorphic and Entire Functions · Advanced Mathematical Identities
