Ramanujan's Harmonic Number Expansion
Classical Analysis and ODEs
2007-05-23 v2
Abstract
An algebraic transformation of the DeTemple-Wang half-integer approximation to the harmonic series produces the general formula and error estimate for the Ramanujan expansion for the nth harmonic number.
Keywords
Cite
@article{arxiv.math/0511335,
title = {Ramanujan's Harmonic Number Expansion},
author = {Mark B. Villarino},
journal= {arXiv preprint arXiv:math/0511335},
year = {2007}
}
Comments
7 pages. Acknowledgements added. Many typos corrected. Parts of the proof rewritten