@article{article_1516291, title={(q,h)-Bernstein Bases and Basic Hypergeometric Series}, journal={Journal of Engineering Technology and Applied Sciences}, volume={10}, pages={63–70}, year={2025}, DOI={10.30931/jetas.1516291}, author={Zürnacı Yetiş, Fatma}, keywords={Quantum Bernstein bases, Marsden identity, basic hypergeometric series, q-Chu-Vandermonde formula, q-Pfaff-Saalschütz formula}, 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.}, number={1}, publisher={Muhammet KURULAY}