Extension of the Bertrand-De Morgan test and its application

2019/01/31 by Vyacheslav M. Abramov · 2 citations
Computer Science · Mathematics · #Bachelor #Bayesian Methods and Mixture Models #Convergence (economics) #Extension (predicate logic) #Random Matrices and Applications #Simple (philosophy) #Stochastic processes and statistical mechanics #Test (biology) #math.GM #msc:40A05 #msc:41A60 #msc:60J80

paper · pdf · doi:10.1080/00029890.2020.1722551

published as The American Mathematical Monthly, 127 (2020) 444--448 · Prepublished version

openalex created_date 2019/08/22 · openalex publication_date 2020/04/23 · arxiv created 2021/04/09 · arxiv updated 2021/04/13 · openalex updated_date 2026/08/05

Abstract

We provide a simple proof for the extended Bertrand-De Morgan test that was earlier studied in [F. Ďuriš, Infinite Series: Convergence tests. Bachelor thesis, 2009] and [A.A. Tabatabai Adnani, A. Reza and M. Morovati, J. Lin. Topol. Algebra, 2 (3), pp. 141--147 (2013)] and demonstrate an application of that test in the theory of birth-and-death processes and random walks.

Cited by

• Evaluating the sum of convergent positive series
• Ratio test [wikipedia]

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