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

Zurnaci F., Goldman R., Simeonov P.

FILOMAT, cilt.34, sa.8, ss.2485-2494, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 8
  • Basım Tarihi: 2020
  • Doi Numarası: 10.2298/fil2008485z
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.2485-2494
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

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.