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

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 re...

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Bibliographic Details
Main Authors: Yilmaz Simsek, Mehmet Acikgoz
Format: Article
Language:English
Published: Wiley 2010-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2010/769095
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Summary: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.
ISSN:1085-3375
1687-0409