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International Journal of Mathematics and Mathematical Sciences
Volume 2006, Article ID 53474, 20 pages
http://dx.doi.org/10.1155/IJMMS/2006/53474

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 Hindawi Publishing Corporation. 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.

Abstract

The classical least squares solutions in C[1,1] in terms of linear combinations of ultraspherical polynomials are extended in order to estimate power series on (1,1). 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.