Mathematics – Classical Analysis and ODEs
Scientific paper
2004-02-22
Mathematics
Classical Analysis and ODEs
7 pages. Numerical copy error corrected as well as the computations based on it. Minor expository improvements
Scientific paper
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.
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