Hankel Transform of the First Form (q,r)-Dowling Numbers

TL;DR

This paper derives the Hankel transform of the first form (q, r)-Dowling numbers by extending methods used for generalized q-exponential polynomials and (q, r)-Whitney numbers.

Contribution

It introduces a novel application of Cigler's method to compute the Hankel transform of (q, r)-Dowling numbers, linking them to generalized q-exponential polynomials.

Findings

Hankel transform of (q, r)-Dowling numbers is explicitly obtained.

Method extends Cigler's approach to new classes of numbers.

Provides a new perspective on the structure of (q, r)-Dowling numbers.

Abstract

In this paper, the Hankel transform of the generalized q-exponential polynomial of the first form (q, r)-Whitney numbers of the second kind is established using the method of Cigler. Consequently, the Hankel transform of the first form (q, r)-Dowling numbers is obtained as special case.