Basic hypergeometric formulas and identities for negative degree q-Bernstein bases

TUNCER O. O., Simeonov P., Goldman R.

Filomat, vol.38, no.8, pp.2941-2948, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 8
  • Publication Date: 2024
  • Doi Number: 10.2298/fil2408941o
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2941-2948
  • Keywords: basic hypergeometric series, Negative degree q-Bernstein bases, q-Gauss formula, q-Marsden identity
  • Hacettepe University Affiliated: Yes


We utilize formulas for basic hypergeometric series to derive identities and formulas for negative degree q-Bernstein bases, including the Marsden identity, the partition of unity property, the monomial representation formula, the reparametrization formula, and the degree reduction formula. We show that all these identities are just special forms of the q-analogue of Gauss’ formula. We also provide a new proof for the q-analogue of Gauss’ formula by using the Marsden identity for negative degree q-Bernstein bases together with the identity theorem for analytic functions.