Generating Functions for the $q$-Bernstein Bases

DOI10.1137/130921623zbMath1304.65264OpenAlexW2034193124MaRDI QIDQ2935255

Yilmaz Simsek, Plamen C. Simeonov, Ronald N. Goldman

Publication date: 22 December 2014

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/130921623

zbMATH Keywords

generating functions\(q\)-calculus\(q\)-Bernstein bases\(q\)-exponential functions\(q\)-Bézier curves

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Computer-aided design (modeling of curves and surfaces) (65D17) Polynomials and rational functions of one complex variable (30C10) Numerical methods for functional equations (65Q20)

Related Items (13)

A note on \((p,q)\)-Bernstein polynomials and their applications based on \((p,q)\)-calculus ⋮ Analysis of the Bernstein basis functions: an approach to combinatorial sums involving binomial coefficients and Catalan numbers ⋮ Approximation properties of \(q\)-Bernoulli polynomials ⋮ On the generating functions and special functions associated with superoscillations ⋮ An evaluation algorithm for \(q\)-Bézier triangular patches formed by convex combinations ⋮ A p-DEFORMED q-INVERSE PAIR AND ASSOCIATED POLYNOMIALS INCLUDING ASKEY SCHEME ⋮ Best polynomial degree reduction on \(q\)-lattices with applications to \(q\)-orthogonal polynomials ⋮ Multidimensional Bernstein polynomials and Bézier curves: analysis of machine learning algorithm for facial expression recognition based on curvature ⋮ Some approximation properties of new Kantorovich type \(q\)-analogue of Balázs-Szabados operators ⋮ \(q\)-analogues and properties of the Laplace-type integral operator in the quantum calculus theory ⋮ Some approximation properties of new \(( p,q ) \)-analogue of Balázs-Szabados operators ⋮ Some recurrence formulas for the q-Bernoulli and q-Euler polynomials ⋮ Accurate Computations with Collocation Matrices of q-Bernstein Polynomials

This page was built for publication: Generating Functions for the $q$-Bernstein Bases