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

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dc.creatorVillarino, Mark B.
dc.date2004-02-22
dc.date2005-05-25
dc.date.accessioned2026-07-07T05:05:38Z
dc.date.available2026-07-07T05:05:38Z
dc.descriptionA 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.
dc.description7 pages. Numerical copy error corrected as well as the computations based on it. Minor expository improvements
dc.identifierhttps://arxiv.org/abs/math/0402354
dc.identifierhttp://arxiv.org/abs/math/0402354
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70240
dc.subjectClassical Analysis and ODEs
dc.subject40A25
dc.titleRamanujan's Approximation to the nth Partial Sum of the Harmonic Series
dc.typetext

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