A New Generating Function of (q-) Bernstein-Type Polynomials and Their Interpolation Function

作者：Simsek Yilmaz; Acikgoz Mehmet^*

来源：Abstract and Applied Analysis, 2010, 2010: 769095.

DOI：10.1155/2010/769095

The main object of this paper is to construct a new generating function of the (q-) Bernsteintype 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.

• 出版日期2010