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arXiv 2104.01702math.CAmath.PR
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正项级数收敛的充要条件

Necessary and sufficient conditions for the convergence of positive series

Vyacheslav M. Abramov

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"
发表信息：
Journal of Classical Analysis. 19 (2022), 117--125
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摘要：

本文发展了[M]中的Bertran-De Morgan和Cauchy型判别法，给出了正项级数收敛的新的充要条件。Martin，Bull.Amer.Math.Soc.47（1941），452-457]和[L. Bourchtein等人，Int.J.Math.Anal. 6（2012），1847-1869]。所得结果使我们推广了[V.M. Abramov，Amer. Math. Monthly 127（2020）444-448]。

英文摘要：

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].

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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