Harmonic number identities via polynomials with r-Lah coefficients

Abstract

Identités sur les nombres harmonique via des polynômes à coefficients r-Lah

Generalized harmonic numbers via poly-Bernoulli polynomials

“…Hence, the proof follows from ( 8) and ( 9). ( 32) follows similarly by using the generating function [25] ∞ k=0 h (k+1)…”

“…Harmonic numbers naturally find places in mathematics and applications such as combinatorics, mathematical analysis, number theory, computer sciences. Therefore, introducing new representations and closed forms for harmonic numbers and their generalizations ( [5,17,16,39]), evaluating series involving harmonic numbers ( [1,8,21,32,36,37]), and relating harmonic numbers with other subjects ( [7,12,25,26,35]) are active research areas.…”

“…Among many other generalizations of harmonic numbers, we are interested in a unified generalization, the generalized hyperharmonic numbers, defined as [17] H (p,r) There is an extensive literature on harmonic and hyperharmonic numbers. Among which we emphasize the formulas [12] (see also [7,25,35])…”

Poly-Cauchy Numbers with Higher Level

“…Another of the most famous generalized Stirling numbers is the r-Stirling number [11], which has meaningful relations with harmonic numbers from the summation formulas [12][13][14]. By using r-Stirling numbers, so-called various r-numbers are introduced.…”

Several recurrence relations and identities on generalized derangement numbers

“…For further investigations concerning with generalized harmonic numbers, the readers may consult with [1,2,4,7,10,11,27,28] and references cited therein.…”