Hankel Transform of the Type 2 (<i>p</i>,<i>q</i>)-Analogue of <i>r</i>-Dowling Numbers

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.

Keywords

• <i>r</i>-Whitney numbers
• <i>r</i>-Dowling numbers
• A-tableaux
• convolution identities
• binomial transform
• Hankel transform