Submitted:
16 December 2017
Posted:
18 December 2017
You are already at the latest version
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
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