Relationships between identities for quantum Bernstein bases and formulas for hypergeometric series

DOI10.2298/FIL2008485ZzbMath1499.65063MaRDI QIDQ5866185

Fatma Zürnacı, Plamen C. Simeonov, Ronald N. Goldman

Publication date: 13 June 2022

Published in: Filomat (Search for Journal in Brave)

zbMATH Keywords

hypergeometric seriesMarsden identityChu-Vandermonde formulaPfaff-Saalschütz formulaquantum Bernstein bases

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Computer-aided design (modeling of curves and surfaces) (65D17) Classical hypergeometric functions, ({}_2F_1) (33C05)

Cites Work

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• \(h\)-blossoming: A new approach to algorithms and identities for \(h\)-Bernstein bases and \(h\)-Bézier curves
• \(q\)-blossoming: A new approach to algorithms and identities for \(q\)-Bernstein bases and \(q\)-Bézier curves
• A de Casteljau algorithm for generalized Bernstein polynomials
• Shape parameter deletion for Pólya curves
• Interpolation and approximation by polynomials
• \(q\)-Bernstein polynomials and Bézier curves
• A polynomial blossom for the Askey-Wilson operator
• Polya’s Urn Model and Computer Aided Geometric Design
• A generalization of the Bernstein polynomials
• A survey of results on the q-Bernstein polynomials
• Generalized Bernstein polynomials

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