Generalized q-Stirling Numbers and Their Interpolation Functions

Abstract

In this paper, we define the generating functions for the generalized q-Stirling numbers of the second kind. By applying Mellin transform to these functions, we construct interpolation functions of these numbers at negative integers. We also derive some identities and relations related to q-Bernoulli numbers and polynomials and q-Stirling numbers of the second kind.

Keywords

• q-Bernoulli numbers and polynomials
• generalized q-Stirling numbers of the second kind
• q-zeta function