Open Access

Derivatives of Integrating Functions for Orthonormal Polynomials with Exponential-Type Weights

Journal of Inequalities and Applications20092009:528454

https://doi.org/10.1155/2009/528454

Received: 22 December 2008

Accepted: 22 April 2009

Published: 4 May 2009

Abstract

Let , , where is an even function. In 2008 we have a relation of the orthonormal polynomial with respect to the weight ; , where and are some integrating functions for orthonormal polynomials . In this paper, we get estimates of the higher derivatives of and , which are important for estimates of the higher derivatives of .

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Authors’ Affiliations

(1)
Department of Mathematics Education, Sungkyunkwan University
(2)

Copyright

© H. S. Jung and R. Sakai 2009

This article is published under license to BioMed Central Ltd. 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.