GENERATING FUNCTIONS FOR THE q-BERNSTEIN BASES


Goldman R., Simeonov P., ŞİMŞEK Y.

SIAM JOURNAL ON DISCRETE MATHEMATICS, vol.28, no.3, pp.1009-1025, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 3
  • Publication Date: 2014
  • Doi Number: 10.1137/130921623
  • Journal Name: SIAM JOURNAL ON DISCRETE MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1009-1025
  • Keywords: q-Bernstein bases, generating functions, q-exponential functions, q-calculus, q-Bezier curves, IDENTITIES, ALGORITHMS
  • Akdeniz University Affiliated: Yes

Abstract

We derive explicit formulas for the generating functions of the q-Bernstein basis functions in terms of q-exponential functions. Using these explicit formulas, we derive a collection of functional equations for these generating functions which we apply to prove a variety of identities, some old and some new, for the q-Bernstein bases.