On the Ramanujan–Lodge harmonic number expansion
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Authors
Mortici, Cristinel
Villarino, Mark Bertram
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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.
Description
Keywords
Harmonic numbers, Bernoulli numbers, Asymptotic expansion, Rate of convergence, Approximations, Inequalities, Matemáticas, 510 Matemáticas