Combinatorial Identities Associated with Bernstein Type Basis Functions


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ŞİMŞEK Y.

FILOMAT, vol.30, no.7, pp.1683-1689, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 7
  • Publication Date: 2016
  • Doi Number: 10.2298/fil1607683s
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1683-1689
  • Keywords: Bernstein polynomials, Generating function, Beta type polynomials, Gamma function, Beta function, Binomial coefficients, Combinatorial sums, Catalan numbers, POLYNOMIALS
  • Akdeniz University Affiliated: Yes

Abstract

In this paper, we give some identities and relations for the Bernstein basis functions and the beta type polynomials. Integrating these identities, we derive many identities and formulas, some old and some new, for combinatorial sums involving binomial coefficients and the Catalan numbers. We also give remarks and comments on these identities.