正级数收敛的充要条件

Journal of classical analysis Pub Date : 2021-04-04 DOI:10.7153/jca-2022-19-09

V. Abramov

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引用次数: 2

摘要

本文发展了文献[M]中的Bertran-De Morgan和Cauchy型判别，给出了正级数收敛的新的充分必要条件。马丁,公牛。阿米尔。数学。社会科学，47(1941)，45 - 24 [L]。Bourchtein et al .;j .数学。植物学报，6(2012)，1847-1869。所得结果推广了文献[V]中关于生死过程递归性和暂态性的已知条件。阿布拉莫夫，美国数学。月刊127(2020)444-448]。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Necessary and sufficient conditions for the convergence of positive series

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), 452457] 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].

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