Integration of Jacobi and Weighted Bernstein Polynomials Using Bases Transformations

Abstract

This paper presents methods to compute integrals of the Jacobi polynomials by the representation in terms of the Bernstein — Bézier basis. We do this because the integration of the Bernstein — Bézier form simply corresponds to applying the de Casteljau algorithm in an easy way. Formulas for the definite integral of the weighted Bernstein polynomials are also presented. Bases transformations are used. In this paper, the methods of integration enable us to gain from the properties of the Jacobi and Bernstein bases. © 2007, Institute of Mathematics, NAS of Belarus. All rights reserved.