Beta-type polynomials and their generating functions

Simsek Y.

APPLIED MATHEMATICS AND COMPUTATION, vol.254, pp.172-182, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 254
  • Publication Date: 2015
  • Doi Number: 10.1016/j.amc.2014.12.118
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.172-182
  • Keywords: Bernstein basis functions, Generating function, Beta polynomials, Beta function and Gamma function, Laplace transform, Combinatorial identity, INVERSES, ZETA, SUMS
  • Akdeniz University Affiliated: Yes

Abstract

We construct generating functions for beta-type rational functions and the beta polynomials. By using these generating functions, we derive a collection of functional equations and PDEs. By using these functional equations and PDEs, we give derivative formulas, a recurrence relation and a variety of identities related to these polynomials. We also give a relation between the beta-type rational functions and the Bernstein basis functions. Integrating these identities and relations, we derive various combinatorial sums involving binomial coefficients, some old and some new, for the beta-type rational functions and the Bernstein basis functions. Finally, by applying the Laplace transform to these generating functions, we obtain two series representations for the beta-type rational functions. (C) 2014 Elsevier Inc. All rights reserved.