Ramanujan's Approximation to the nth Partial Sum of the Harmonic Series
经典分析与常微分方程
2007-05-23 v5
摘要
A simple integration by parts and telescopic cancellation leads to a rigorous derivation of the first 2 terms for the error in Ramanujan's asymptotic series for the nth partial sum of the harmonic series. Then Kummer's transformation gives three more terms and a rigorous error estimate. Finally best-possible estimates of Lodge's approximations.
引用
@article{arxiv.math/0402354,
title = {Ramanujan's Approximation to the nth Partial Sum of the Harmonic Series},
author = {Mark B. Villarino},
journal= {arXiv preprint arXiv:math/0402354},
year = {2007}
}
备注
7 pages. Numerical copy error corrected as well as the computations based on it. Minor expository improvements