On a method of approximation by Jacobi polynomials

Abstract

Convolution structure for Jacobi series allows end point summability of Fourier-Jacobi expansions to lead an approximation of function by a linear combination of Jacobi polynomials. Thus, using Ces$\grave a$ro summability of some orders $>1$ at $x=1,$ we prove a result of approximation of functions on $[-1,1]$ by operators involving Jacobi polynomials. Precisely, we pick up functions from a Lebesgue integrable space and then study its representation by Jacobi polynomials under different conditions.