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arXiv:math/0402354 [math.CA]AbstractReferencesReviewsResources

Ramanujan's Approximation to the nth Partial Sum of the Harmonic Series

Mark B. Villarino

Published 2004-02-22, updated 2005-05-25Version 5

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.

Comments: 7 pages. Numerical copy error corrected as well as the computations based on it. Minor expository improvements
Categories: math.CA
Subjects: 40A25
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