Formulae relating littleq-Jacobi,q-Hahn andq-Bernstein polynomials: application toq-Bézier curve evaluation

DOI10.1080/10652460410001727491zbMath1065.33010OpenAlexW2155301614MaRDI QIDQ4822861

André Ronveaux, Paweł Woźny, Stanisław Lewanowicz, IvÁn Area, Eduardo Paciência Godoy

Publication date: 25 October 2004

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460410001727491

zbMATH Keywords

\(q\)-orthogonal polynomials\(q\)-Bernstein polynomials\(q\)-Hahn polynomialsBasic hypergeometric seriesLittle \(q\)-Jacobi polynomials

Mathematics Subject Classification ID

Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (5)

Dual generalized Bernstein basis ⋮ Representation of \((p,q)\)-Bernstein polynomials in terms of \((p,q)\)-Jacobi polynomials ⋮ Best polynomial degree reduction on \(q\)-lattices with applications to \(q\)-orthogonal polynomials ⋮ Quantum Lorentz degrees of polynomials and a Pólya theorem for polynomials positive on \(q\)-lattices ⋮ ON EXISTENCE OF SOLUTIONS FOR NONLINEAR Q-DIFFERENCE EQUATIONS WITH NONLOCAL Q-INTEGRAL BOUNDARY CONDITIONS

Cites Work

• \(q\)-Bernstein polynomials and Bézier curves
• Construction of recurrences for the coefficients of expansions in \(q\)-classical orthogonal polynomials
• Recurrence relations for the coefficients of the Fourier series expansions with respect to q-classical orthogonal polynomials
• Explicit Formula Relating the Jacobi, Hahn and Bernstein Polynomials
• Bernstein bases and hahn—eberlein orthogonal polynomials

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