Change of basis for generalized Chebyshev Koornwinder's type polynomials of first kind

TL;DR

This paper derives an explicit expression for generalized Chebyshev Koornwinder's type polynomials of the first kind in Bernstein basis and explores the basis change between these polynomials and Bernstein polynomials.

Contribution

It provides a new explicit form of these polynomials in Bernstein basis and analyzes the basis transformation, enhancing understanding of their structural relationship.

Findings

Explicit form of polynomials in Bernstein basis

Analysis of basis change between polynomials and Bernstein basis

Potential applications in approximation theory

Abstract

In this paper an explicit form of generalized Chebyshev Koornwinder's type polynomial of first kind in terms of the Bernstein basis of fixed degree $n$ is provided. Moreover, we investigate generalized Chebyshev Koornwinder's type polynomials of first kind and Bernstein polynomials change of bases.