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

Year 2025, Volume: 10 Issue: 1, 63 - 70, 29.04.2025

Fatma Zürnacı Yetiş

https://doi.org/10.30931/jetas.1516291

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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