𝑞-Bernstein Polynomials Associated with 𝑞-Stirling Numbers and Carlitz's 𝑞-Bernoulli Numbers - T. Kim; J. Choi; Y. H. Kim (Abstract and Applied Analysis)
Recently, Kim (2011) introduced 𝑞-Bernstein polynomials which are different 𝑞-Bernstein polynomials of Phillips (1997). In this paper, we give a 𝑝-adic 𝑞-integral representation for 𝑞-Bernstein type polynomials and investigate some interesting identities of 𝑞-Bernstein type polynomials associated with 𝑞-extensions of the binomial distribution, 𝑞-Stirling numbers, and Carlitz's 𝑞-Bernoulli numbers.