(q,h)-Bernstein Bases and Basic Hypergeometric Series

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Journal of Engineering Technology and Applied Sciences
Cilt: 10 Sayı: 1
(q,h)-Bernstein Bases and Basic Hypergeometric Series

(q,h)-Bernstein Bases and Basic Hypergeometric Series

Pages : 63-70

View : 69 | Download : 26

Publication Date : 2025-04-29

Article Type : Research Paper

Abstract :Quantum (q,h)-Bernstein bases and basic hypergeometric series are two seemingly unrelated mathematical entities. In this work, it is indicated that they are deeply interrelated theories. This new insight into two theories enables the provision of new proofs for two basic hypergeometric sums. The q-Chu-Vandermonde formula for basic hypergeometric series is proved by the partition of unity property for (q,h)-Bernstein bases, and the q-Pffaf-Saalschütz formula for basic hypergeometric series is proved by the Marsden identity for (q,h)-Bernstein bases.
Keywords : Quantum Bernstein bases, Marsden identity, basic hypergeometric series, q-Chu-Vandermonde formula, q-Pfaff-Saalschütz formula

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