A New Generating Function of (q-) Bernstein-Type Polynomials and Their Interpolation Function

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ŞİMŞEK Y., Acikgoz M.

ABSTRACT AND APPLIED ANALYSIS, vol.2010, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2010
  • Publication Date: 2010
  • Doi Number: 10.1155/2010/769095
  • Journal Name: ABSTRACT AND APPLIED ANALYSIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Akdeniz University Affiliated: Yes

Abstract

The main object of this paper is to construct a new generating function of the (q-) Bernsteintype 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.