Relationships Between Identities for Quantum Bernstein Bases and Formulas for Hypergeometric Series

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Zürnacı Yetiş F., Goldman R., Simeonov P.

FILOMAT, vol.34, no.8, pp.2485-2494, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 8
  • Publication Date: 2020
  • Doi Number: 10.2298/fil2008485z
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.2485-2494
  • Keywords: Quantum Bernstein bases, Marsden identity, hypergeometric series, Chu-Vandermonde formula, Pfaff-Saalschutz formula, ALGORITHMS
  • Dokuz Eylül University Affiliated: No

Abstract

Two seemingly disparate mathematical entities - quantum Bernstein bases and hypergeometric series - are revealed to be intimately related. The partition of unity property for quantum Bernstein bases is shown to be equivalent to the Chu-Vandermonde formula for hypergeometric series, and the Marsden identity for quantum Bernstein bases is shown to be equivalent to the Pfaff-Saalschutz formula for hypergeometric series. The equivalence of the q-versions of these formulas and identities is also demonstrated.