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Advances in Numerical Analysis
Volume 2013 (2013), Article ID 263467, 8 pages
http://dx.doi.org/10.1155/2013/263467
Research Article

A New Extended Padé Approximation and Its Application

1Department of Mathematics, Birjand University, Birjand, Iran
2Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran

Received 19 June 2013; Revised 16 September 2013; Accepted 7 October 2013

Academic Editor: Weimin Han

Copyright © 2013 Z. Kalateh Bojdi et al. 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

We extend ordinary Padé approximation, which is based on a set of standard polynomials as , to a new extended Padé approximation (Müntz Padé approximation), based on the general basic function set    (the particular case of Müntz polynomials) using general Taylor series (based on fractional calculus) with error convergency. The importance of this extension is that the ordinary Padé approximation is a particular case of our extended Padé approximation. Also the parameterization ( is the corresponding parameter) of new extended Padé approximation is an important subject which, obtaining the optimal value of this parameter, can be a good question for a new research.