A new generating function of (q-) Bernstein-type polynomials and their interpolation function

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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. © 2010 Y. Simsek and M. Acikgoz.

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Acikgoz, M., & Simsek, Y. (2010). A new generating function of (q-) Bernstein-type polynomials and their interpolation function. Abstract and Applied Analysis, 2010. https://doi.org/10.1155/2010/769095

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