New properties of a certain method of summation of generalized hypergeometric series

TL;DR

This paper provides a theoretical analysis and convergence acceleration theorem for a summation method of generalized hypergeometric series, supported by new results and numerical examples.

Contribution

It offers new theoretical insights and a convergence acceleration theorem for a summation method applied to generalized hypergeometric series.

Findings

Established convergence acceleration theorem for the method

Provided new theoretical results on the summation technique

Included illustrative numerical examples demonstrating effectiveness

Abstract

In a recent paper (Appl. Math. Comput. 215, 1622--1645, 2009), the authors proposed a method of summation of some slowly convergent series. The purpose of this note is to give more theoretical analysis for this transformation, including the convergence acceleration theorem in the case of summation of generalized hypergeometric series. Some new theoretical results and illustrative numerical examples are given.