GENERATING FUNCTIONS FOR THE q-BERNSTEIN BASES

Goldman R., Simeonov P., ŞİMŞEK Y.

SIAM JOURNAL ON DISCRETE MATHEMATICS, cilt.28, sa.3, ss.1009-1025, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 28 Sayı: 3
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1137/130921623
  • Dergi Adı: SIAM JOURNAL ON DISCRETE MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1009-1025
  • Anahtar Kelimeler: q-Bernstein bases, generating functions, q-exponential functions, q-calculus, q-Bezier curves, IDENTITIES, ALGORITHMS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.