Preprint Article Version 1 This version is not peer-reviewed

On (q, r, w)-Stirling Numbers of the Second Kind

Version 1 : Received: 16 December 2017 / Approved: 18 December 2017 / Online: 18 December 2017 (08:22:41 CET)

How to cite: Duran, U.; Acikgoz, M.; Araci, S. On (q, r, w)-Stirling Numbers of the Second Kind. Preprints 2017, 2017120115 (doi: 10.20944/preprints201712.0115.v1). Duran, U.; Acikgoz, M.; Araci, S. On (q, r, w)-Stirling Numbers of the Second Kind. Preprints 2017, 2017120115 (doi: 10.20944/preprints201712.0115.v1).

Abstract

In this paper, we introduce a new generalization of the r-Stirling numbers of the second kind based on the q-numbers via an exponential generating function. We investigate their some properties and derive several relations among q-Bernoulli numbers and polynomials, and newly de…ned (q, r, w)-Stirling numbers of the second kind. We also obtain q-Bernstein polynomials as a linear combination of (q, r, w)-Stirling numbers of the second kind and q-Bernoulli polynomials in w.

Subject Areas

q-calculus; stirling numbers of the second kind; bernoulli polynomials and numbers; generating function; cauchy product

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