Construction a new generating function of Bernstein type polynomials


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Simsek Y.

APPLIED MATHEMATICS AND COMPUTATION, vol.218, no.3, pp.1072-1076, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 218 Issue: 3
  • Publication Date: 2011
  • Doi Number: 10.1016/j.amc.2011.01.074
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1072-1076
  • Keywords: Generating function, Bernstein polynomials, Bernoulli polynomials of higher-order, Stirling numbers of the second kind, Mellin transformation, Gamma function, Beta function, Bezier curve
  • Akdeniz University Affiliated: Yes

Abstract

Main purpose of this paper is to reconstruct generating function of the Bernstein type polynomials. Some properties of 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 by Mellin transformation. This function interpolates these polynomials at negative integers which are given explicitly. Moreover, relations between these polynomials, the Stirling numbers of the second kind and Bernoulli polynomials of higher order are given. Furthermore some remarks associated with the Bezier curves are given.

Main purpose of this paper is to reconstruct generating function of the Bernstein type polynomials. Some properties of 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 by Mellin transformation. This function interpolates these polynomials at negative integers which are given explicitly. Moreover, relations between these polynomials, the Stirling numbers of the second kind and Bernoulli polynomials of higher order are given. Furthermore some remarks associated with the Bezier curves are given. (C) 2011 Elsevier Inc. All rights reserved.