Journal of Integer Sequences, Vol. 23 (2020), Article 20.3.2

Harmonic Sums via Euler's Transform: Complementing the Approach of Boyadzhiev

Robert Frontczak
Landesbank Baden-Württemberg (LBBW)
Am Hauptbahnhof 2
70173 Stuttgart


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.

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(Concerned with sequences A000032 A000045 A001008 A002805.)

Received October 20 2019; revised version received January 21 2020. Published in Journal of Integer Sequences, February 23 2020.

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