正项级数收敛的充要条件
经典分析与常微分方程
2022-04-19 v5 概率论
摘要
我们给出了正项级数收敛的新充要条件，推广了 [M. Martin, Bull. Amer. Math. Soc. 47(1941), 452-457] 与 [L. Bourchtein 等, Int. J. Math. Anal. 6(2012), 1847-1869] 中的 Bertran-De Morgan 与 Cauchy 型判别法。所得结果使我们能够推广 [V. M. Abramov, Amer. Math. Monthly 127(2020) 444-448] 中给出的生灭过程常返与暂态的已知条件。
引用
@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}
}
备注
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"