Open AccessAsymptotic expansion of a finite sum involving harmonic numbers
Author(s) -
Ling Zhu
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
ISSN - 2473-6988
DOI - 10.3934/math.2021168
Subject(s) - harmonic number , mathematics , harmonic , euler's formula , asymptotic expansion , combinatorics , pure mathematics , mathematical analysis , physics , quantum mechanics , riemann hypothesis
In the paper, we obtain asymptotic expansion of the finite sum of some sequences $ S_{n} = \sum_{k = 1}^{n}\left(n^{2}+k\right) ^{-1} $ by using the Euler's standard one of the harmonic numbers.