A Note on Generating Functions for the Unification of the Bernstein Type Basis Functions

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KUCUKOGLU I., ŞİMŞEK Y.

FILOMAT, vol.30, no.4, pp.985-992, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.2298/fil1604985k
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.985-992
  • Keywords: Bernstein type polynomials, Generating function, Knot sequence, Laplace transform, Binomial coefficients, Gamma and Beta functions, Hermite numbers, POLYNOMIALS, BERNOULLI
  • Akdeniz University Affiliated: Yes

Abstract

In [3], Simsek unified generating function of the Bernstein basis functions. In this paper, by using knot sequence, we rewrite generating functions for the unification of the Bernstein type basis functions. By using these generating functions, we also find generating function for the Hermite type numbers. We investigate some properties of this functions and these basis. Finally, we simulate these polynomials with their plots for some selected numerical values.