Generalized harmonic numbers via poly-Bernoulli polynomials

TL;DR

This paper explores the connection between generalized hyperharmonic numbers and poly-Bernoulli polynomials, deriving new identities and congruences that deepen understanding of these mathematical objects.

Contribution

It introduces a novel relationship linking hyperharmonic numbers with poly-Bernoulli polynomials, leading to new identities and congruences.

Findings

Derived numerous identities for hyper-sums

Established several congruences involving hyperharmonic numbers

Connected harmonic and Bernoulli number theories

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.