On the Ramanujan–Lodge harmonic number expansion

Cristinel Mortici and Mark B. Villarino

Applied Mathematics and Computation, 2015, vol. 251, issue C, 423-430

Abstract: The aim of this paper is to extend and refine the Ramanujan–Lodge harmonic number expansion into negative powers of a triangular number. We construct a faster asymptotic series and some new sharp inequalities for the harmonic numbers.

Keywords: Harmonic numbers; Bernoulli numbers; Asymptotic expansion; Rate of convergence; Approximations; Inequalities (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:251:y:2015:i:c:p:423-430

DOI: 10.1016/j.amc.2014.11.088

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