Abstract
In this paper, type 2 (p,q)-analogues of the r-Whitney numbers of the second kind is defined and a combinatorial interpretation in the context of the A-tableaux is given. Moreover, some convolution-type identities, which are useful in deriving the Hankel transform of the type 2 (p,q)-analogue of the r-Whitney numbers of the second kind are obtained. Finally, the Hankel transform of the type 2 (p,q)-analogue of the r-Dowling numbers are established.
Highlights
Several mathematicians were attracted to work on Hankel matrices because of their connections and applications to some areas in mathematics, physics, and computer science
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Material and Method This research was facilitated with the methods employed in the previous study on (p, q)-analogue of Stirling-type and Bell-type numbers and the Hankel transform of some special numbers and functions [2,4,5,8,12,18,27,32,34]
Summary
Several mathematicians were attracted to work on Hankel matrices because of their connections and applications to some areas in mathematics, physics, and computer science. Several theories and applications of these matrices were established including the Hankel determinant and Hankel transform. The notion of Hankel transform was first introduced in Sloane’s sequence A055878 [1] and was later on studied by Layman [2]. The Hankel matrix Hn of order n of a sequence A = {a0, a1, . An} is defined by Received: 19 October 2021 Accepted: 9 December 2021 Published: 16 December 2021. The Hankel determinant hn of order n of A is defined to be the determinant of the corresponding Hankel matrix of order n.
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