Polynomials with r-Lah coefficient and hyperharmonic numbers

TL;DR

This paper introduces new polynomial families involving r-Lah numbers using Mellin derivatives, revealing connections to hyperharmonic numbers and deriving related identities.

Contribution

It presents novel polynomial families involving r-Lah numbers and establishes their relationships with hyperharmonic numbers, leading to new identities.

Findings

New polynomial families involving r-Lah numbers

Connections established between these polynomials and hyperharmonic numbers

Derived identities for harmonic and hyperharmonic numbers

Abstract

In this paper, we take advantage of the Mellin type derivative to produce some new families of polynomials whose coefficients involve r-Lah numbers. One of these polynomials leads to rediscover many of the identities of r-Lah numbers. We show that some of these polynomials and hyperharmonic numbers are closely related. Taking into account of these connections, we reach several identities for harmonic and hyperharmonic numbers.