More Asymptotic Expansions for the Harmonic Numbers
Received:May 24, 2019  Revised:March 17, 2020
Key Word: asymptotic expansions   harmonic numbers   Bell polynomials  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11501081).
Author NameAffiliation
Hongmei LIU School of Science, Dalian Minzu University, Liaoning 116600, P. R. China 
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      In this paper, by exponential complete Bell polynomials, we establish a (general) harmonic number asymptotic expansion, and give the corresponding recurrence of the coefficient sequence in the expansion. By the methods of the generating functions and summation transformations, we also present an explicit expression for the coefficient sequence of the expansion. Moreover, we establish two (general) lacunary harmonic number asymptotic expansions, which contain only even or odd power terms in the logarithmic term.
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