Construction a new generating function of Bernstein type polynomials

Details Construction a new generating function of Bernstein type polynomials Construction a new generating function of Bernstein type polynomials

2010-10-18

arxiv.org/abs/1010.3711v1

Applied Mathematics and Computation 218 (2011) 1072-1076

Mathematics

Classical Analysis and ODEs

7 pages

Scientific paper

10.1016/j.amc.2011.01.074

Main purpose of this paper is to reconstruct generating function of the Bernstein type polynomials. Some properties this generating functions are given. By applying this generating function, not only derivative of these polynomials but also recurrence relations of these polynomials are found. Interpolation function of these polynomials is also constructed via Mellin Transformation. This function interpolates these polynomials at negative integers which are given explicitly. Moreover, relations between these polynomials, the generalized Stirling numbers, and Bernoulli polynomials of higher order are given. Furthermore some applications associated with B\'ezier curve are given.

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