On the Generating Function for Bernstein Polynomials

2010/01/01 by Mehmet Açıkgöz, Serkan Aracı, Theodore E. Simos +2 · 2 citations
Mathematics · Computer Science · #Approximation Theory and Sequence Spaces #Advanced Mathematical Identities #Advanced Algebra and Logic #Bernstein polynomial #Function (biology) #Generating function #Recurrence relation #Difference polynomials #Applied mathematics #Derivative (finance) #Mathematics #Computer science #Orthogonal polynomials #Algebra over a field #Pure mathematics #Discrete mathematics #Combinatorics

paper · doi:10.1063/1.3497855

openalex publication_date 2010/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

The aim of this paper is to give main properties of the generating function of the Bernstein polynomials. We prove recurrence relations and derivative formula for Bernstein polynomials. Furthermore, some new results are obtained by using this generating function of these polynomials.

Citations

• Iterated Bernstein polynomial approximations
• q-Bernoulli Numbers and Polynomials Associated with Multiple q-Zeta Functions and Basic L-series

Cited by

• Functional equations from generating functions: a novel approach to deriving identities for the Bernstein basis functions
• Bernstein polynomial [wikipedia]

Related

• Degenerate Bernstein Polynomials
• Differential-recurrence properties of dual Bernstein polynomials
• Note on the Modified q-Bernstein Polynomials
• A Method for Obtaining Polynomials of Bernstein Type of Two Variables
• Fast and accurate evaluation of dual Bernstein polynomials