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Asymptotic Behavior of Remainders of Special Number Series

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dc.contributor.authorKostin, A. B.
dc.contributor.authorSherstyukov, V. B.
dc.contributor.authorКостин, Андрей Борисович
dc.date.accessioned2024-11-27T10:05:18Z
dc.date.available2024-11-27T10:05:18Z
dc.date.issued2020
dc.description.abstract© 2020, Springer Science+Business Media, LLC, part of Springer Nature.We consider a one-parameter family of number series involving the generalized harmonic series and study asymptotic properties of the remainders. Using R(Np)≡∑n=N∞1/np as an example, we describe the typical obtained results: we obtain the integral representation, find the complete asymptotic expansion with respect to the parameter 2N − 1 as N →∞, and prove that R(N, p) is enveloped by its asymptotic series. The possibilities of the proposed approach are demonstrated by the problem of exact two-sided estimates for the central binomial coefficient.
dc.identifier.citationKostin, A. B. Asymptotic Behavior of Remainders of Special Number Series / Kostin, A.B., Sherstyukov, V.B. // Journal of Mathematical Sciences (United States). - 2020. - 10.1007/s10958-020-05131-2
dc.identifier.doi10.1007/s10958-020-05131-2
dc.identifier.urihttps://www.doi.org/10.1007/s10958-020-05131-2
dc.identifier.urihttps://www.scopus.com/record/display.uri?eid=2-s2.0-85096343677&origin=resultslist
dc.identifier.urihttps://openrepository.mephi.ru/handle/123456789/22611
dc.relation.ispartofJournal of Mathematical Sciences (United States)
dc.titleAsymptotic Behavior of Remainders of Special Number Series
dc.typeArticle
dspace.entity.typePublication
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relation.isAuthorOfPublication.latestForDiscovery3070740c-c832-420c-a070-a880195523bc
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