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. Preprints2017, 2017120115. https://doi.org/10.20944/preprints201712.0115.v1
Duran, U.; Acikgoz, M.; Araci, S. On (q, r, w)-Stirling Numbers of the Second Kind. Preprints 2017, 2017120115. https://doi.org/10.20944/preprints201712.0115.v1
Duran, U.; Acikgoz, M.; Araci, S. On (q, r, w)-Stirling Numbers of the Second Kind. Preprints2017, 2017120115. https://doi.org/10.20944/preprints201712.0115.v1
APA Style
Duran, U., Acikgoz, M., & Araci, S. (2017). On (<em>q, r, w</em>)-Stirling Numbers of the Second Kind. Preprints. https://doi.org/10.20944/preprints201712.0115.v1
Chicago/Turabian Style
Duran, U., Mehmet Acikgoz and Serkan Araci. 2017 "On (<em>q, r, w</em>)-Stirling Numbers of the Second Kind" Preprints. https://doi.org/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.
Keywords
q-calculus; stirling numbers of the second kind; bernoulli polynomials and numbers; generating function; cauchy product
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
