Polynomials with r-Lah coefficient 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.

References in corpus (7)

• Apostol-Bernoulli functions, derivative polynomials and Eulerian polynomials
• Geometric Polynomials: Properties and Applications to Series with Zeta Values
• Polynomials Related to Harmonic Numbers and Evaluation of Harmonic Number Series I
• Extended Bernoulli and Stirling matrices and related combinatorial identities
• Some integral representations and properties of Lah numbers
• Higher order generalized geometric polynomials
• Euler sums of generalized hyperharmonic numbers

Cited by in corpus (1)

• Recurrence relations of poly-Cauchy numbers by the $r$-Stirling transform