Harmonic Sums via Euler's Transform: Complementing the Approach of Boyadzhiev
Landesbank Baden-Württemberg (LBBW)
Am Hauptbahnhof 2
We prove a new expression for binomial sums with harmonic numbers. Our
derivation is based on an alternative argument for the Euler transform
of these sums. The findings complement a result of Boyadzhiev. To
demonstrate the usefulness of our alternative approach, several examples
are discussed. We rediscover some known identities for harmonic numbers
and present some new ones. In particular, we derive some new identities
involving harmonic numbers, and Fibonacci and Lucas numbers.
Full version: pdf,
(Concerned with sequences
Received October 20 2019; revised version received January 21 2020.
Published in Journal of Integer Sequences,
February 23 2020.
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