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

Yilmaz Simsek and Mehmet Acikgoz

Abstract and Applied Analysis, 2010, vol. 2010, 1-12

Abstract:

The main object of this paper is to construct a new generating function of the ( ) Bernstein-type polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and derivative of the ( ) Bernstein-type polynomials. We also give relations between the ( ) 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 ( ) Bernstein-type polynomials. Moreover, we give some applications and questions on approximations of ( ) Bernstein-type polynomials, moments of some distributions in Statistics.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:769095

DOI: 10.1155/2010/769095

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