Asymptotic Behavior of Remainders of Special Number Seriesстатья
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Дата последнего поиска статьи во внешних источниках: 20 апреля 2022 г.
Аннотация:We consider a one-parameter family of number series involving the generalized harmonic series and study asymptotic properties of the remainders. Using R(N,p)≡\sum_{n=N}^{∞} 1/n^p 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.