Open Journal of Mathematical Analysis
Vol. 8 (2024), Issue 1, pp. 18 – 35
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2024.0132
Convergence analysis of tunable product sequences and series with two tuning parameters and two functions
Christophe Chesneau\(^{1,*}\)
\(^{1}\) Department of Mathematics, LMNO, University of Caen-Normandie, 14032 Caen, France.
Copyright © 2024 Christophe Chesneau. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: May 7, 2024 – Accepted: June 28, 2024 – Published: June 30, 2024
Abstract
The study of innovative sequences and series is important in several fields. In this article, we examine the convergence properties of a particular product series that offers adaptability through two parameters and two functions. Based on this analysis, we extend our investigation to a related series. Our main theorems are proved in detail and include several new intermediate results that can be used for other convergence analysis purposes. This is particularly the case for a generalized version of the Riemann sum formula. Several precise examples are presented and discussed, including one related to the gamma function.
Keywords:
mathematical analysis; product sequences; Riemann sum formula; series; Cauchy root convergence rule