Necessary and sufficient conditions for the convergence of positive series
Classical Analysis and ODEs
2022-04-19 v5 Probability
Abstract
We provide new necessary and sufficient conditions for the convergence of positive series developing Bertran-De Morgan and Cauchy type tests given in [M. Martin, Bull. Amer. Math. Soc. 47(1941), 452-457] and [L. Bourchtein et al, Int. J. Math. Anal. 6(2012), 1847-1869]. The obtained result enables us to extend the known conditions for recurrence and transience of birth-and-death processes given in [V. M. Abramov, Amer. Math. Monthly 127(2020) 444-448].
Keywords
Cite
@article{arxiv.2104.01702,
title = {Necessary and sufficient conditions for the convergence of positive series},
author = {Vyacheslav M. Abramov},
journal= {arXiv preprint arXiv:2104.01702},
year = {2022}
}
Comments
9 pages. The paper is substantially revised according to the referee's comments. It is the final version that is accepted for publication to "Journal of Classical Analysis"