A New Generating Function of () Bernstein-Type Polynomials and Their Interpolation Function
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Open Access
- 30 March 2010
- journal article
- research article
- Published by Hindawi Limited in Abstract and Applied Analysis
- Vol. 2010, 1-12
- https://doi.org/10.1155/2010/769095
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.Keywords
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Funding Information
- Akdeniz University
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