A q-Analogue of r-Whitney Numbers of the Second Kind and Its Hankel Transform

2019/07/06 by Roberto B. Corcino, Jay M. Ontolan, Corcino, Roberto B. +5
Mathematics · #05A15 #11B65 #11B73 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #math.CO #msc:05A15 #msc:11B65 #msc:11B73

paper · pdf · doi:10.48550/arxiv.1907.03094

The paper is composed of 13 pages

openalex publication_date 2019/07/06 · openalex created_date 2019/07/12 · arxiv created 2019/07/23 · arxiv updated 2019/07/24 · openalex updated_date 2026/07/28

Abstract

A q-analogue of r-Whitney numbers of the second kind, denoted by W_m,r[n,k]_q, is defined by means of a triangular recurrence relation. In this paper, several fundamental properties for the q-analogue are established including other forms of recurrence relations, explicit formulas and generating functions. Moreover, a kind of Hankel transform for W_m,r[n,k]_q is obtained.

Related

• Explicit Formulas for the First Form (q,r)-Dowling Numbers and (q,r)-Whitney-Lah Numbers
• Hankel Transform of the First Form (q,r)-Dowling Numbers
• On Divisibility Property of Type 2 (p,q)-Analogue of r-Whitney Numbers of the Second Kind
• q-Catalan numbers and q-Narayana polynomials
• The Translated Whitney-Lah Numbers: Generalizations and q-Analogues