Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 421546, 8 pages
Research Article

A Note on Finite Quadrature Rules with a Kind of Freud Weight Function

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

Received 17 December 2008; Accepted 23 April 2009

Academic Editor: Slimane Adjerid

Copyright © 2009 Kamal Aghigh and M. Masjed-Jamei. 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.


We introduce a finite class of weighted quadrature rules with the weight function |x|2aexp(1/x2) on (,) as |x|2aexp(1/x2)f(x)dx=i=1nwif(xi)+Rn[f], where xi are the zeros of polynomials orthogonal with respect to the introduced weight function, wi are the corresponding coefficients, and Rn[f] is the error value. We show that the above formula is valid only for the finite values of n. In other words, the condition a{maxn}+1/2 must always be satisfied in order that one can apply the above quadrature rule. In this sense, some numerical and analytic examples are also given and compared.