A new class of polynomials associated with Bernstein and beta polynomials

Simsek Y.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.37, no.5, pp.676-685, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 5
  • Publication Date: 2014
  • Doi Number: 10.1002/mma.2825
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.676-685
  • Keywords: functional equations, Bernstein polynomials, Mellin transform, interpolation function, matrix representation, polynomials, generating functions, beta polynomials
  • Akdeniz University Affiliated: Yes

Abstract

The purpose of this paper is to define a new class polynomials. Special cases of these polynomials give many famous family of the Bernstein type polynomials and beta polynomials. We also construct generating functions for these polynomials. We investigate some fundamental properties of these functions and polynomials. Using functional equations and generating functions, we derive various identities related to theses polynomials. We also construct interpolation function that interpolates these polynomials at negative integers. Finally, we give a matrix representations of these polynomials. Copyright (c) 2013 John Wiley & Sons, Ltd.