A New Generating Function of (q-) Bernstein Type Polynomials and their Interpolation Function
Number Theory
2018-11-19 v1 Complex Variables
Abstract
The main object of this paper is to construct a new generating function of the (q-) Bernstein type polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and derivative of the (q-) Bernstein type polynomials. We also give relations between the (q-) Bernstein type polynomials, Hermite polynomials, Bernoulli polynomials of higher-order and the second kind Stirling numbers. By applying Mellin transformation to this generating function, we define interpolation of the (q-) Bernstein type polynomials. Moreover, we give some applications and questions on approximations of (q-) Bernstein type polynomials, moments of some distributions in Statistics.
Cite
@article{arxiv.1001.3400,
title = {A New Generating Function of (q-) Bernstein Type Polynomials and their Interpolation Function},
author = {Yilmaz Simsek and Mehmet Acikgoz},
journal= {arXiv preprint arXiv:1001.3400},
year = {2018}
}