Explicit Formulas for the First Form (q,r)-Dowling Numbers and (q,r)-Whitney-Lah Numbers

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v14i1.3900

Keywords:

r-Whitney-Lah numbers, r-Whitney numbers, r-Dowling numbers, generating function, q-exponential function, q-difference operator, Newton’s Interpolation Formula

Abstract

In this paper, a q-analogue of r-Whitney-Lah numbers, also known as (q,r)-Whitney-Lah number, denoted by $L_{m,r} [n, k]_q$ is defined using the triangular recurrence relation. Several fundamental properties for the q-analogue are established such as vertical and horizontal recurrence relations, horizontal and exponential generating functions. Moreover, an explicit formula for (q, r)-Whitney-Lah number is derived using the concept of q-difference operator, particularly, the q-analogue of Newton’s Interpolation Formula (the umbral version of Taylor series). Furthermore, an explicit formula for the first form (q, r)-Dowling numbers is obtained which is expressed in terms of (q,r)-Whitney-Lah numbers and (q,r)-Whitney numbers of the second kind.

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Published

2021-01-31

Issue

Section

Nonlinear Analysis

How to Cite

Explicit Formulas for the First Form (q,r)-Dowling Numbers and (q,r)-Whitney-Lah Numbers. (2021). European Journal of Pure and Applied Mathematics, 14(1), 65-81. https://doi.org/10.29020/nybg.ejpam.v14i1.3900