Generalized harmonic numbers via poly-Bernoulli polynomials

Levent Kargın                <meta name=

2022/100/3-4 (6) — DOI: 10.5486/PMD.2022.9074 — pp. 365-386

Generalized harmonic numbers via poly-Bernoulli polynomials

Authors: Levent Kargın, Mehmet Cenkci, Ayhan Dil and Mümün Can

Abstract:

We present a relationship between the generalized hyperharmonic numbers and the poly-Bernoulli polynomials, motivated from the connections between harmonic and Bernoulli numbers. This relationship yields numerous identities for the hyper-sums and several congruences.

Keywords: harmonic numbers, hyperharmonic numbers, generalized harmonic numbers, poly-Bernoulli polynomials, Stirling numbers, hyper-sums, congruences

Mathematics Subject Classification: 11B75, 11B68, 11B73, 11A07