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.