International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 53474, 20 pages
Least squares approximations of power series
Department of Mathematics, Buffalo State College (SUNY), 1300 Elmwood Avenue, Buffalo 14222-1095, NY, USA
Received 27 June 2005; Revised 12 June 2006; Accepted 22 June 2006
Copyright © 2006 James Guyker. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The classical least squares solutions in in terms of linear combinations of ultraspherical polynomials are extended in
order to estimate power series on (). Approximate rates of
uniform and pointwise convergence are obtained, which correspond to
recent results of U. Luther and G. Mastroianni on Fourier
projections with respect to Jacobi polynomials.