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Özden, Hacer; Cangül, Ismail Naci; Simsek, Yilmaz

Generalized \(q\)-Stirling numbers and their interpolation functions. (English) Zbl 1316.11017

Axioms 2, No. 1, 10-19 (2013).
Summary: 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.

Cited in 2 Documents

MSC:

11B73 Bell and Stirling numbers
11B68 Bernoulli and Euler numbers and polynomials
11S40 Zeta functions and \(L\)-functions
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)

Keywords:

\(q\)-Bernoulli numbers and polynomials; generalized \(q\)-Stirling numbers of the second kind; \(q\)-zeta function
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