On Multiparameter \(q\)-Noncentral Stirling and Bell Numbers

Abstract

The notion of multiparameter \(q\)-noncentral Stirling numbers is introduced by means of a triangular recurrence relation. Some properties for these \(q\)-analogues such as vertical and horizontal recurrence relations, horizontal generating functions, explicit formula, orthogonality and inverse relations are established. Moreover, we introduce the multiparameter Bell numbers and Bell polynomials, their connection to factorial moments and their respective \(q\)-analogues.