Department of Mathematics, K.N. Toosi University of Technology, P.O. Box 1618, Tehran 16315-1618, Iran
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 on as
, where are the zeros of polynomials orthogonal with respect to the introduced weight
function, are the corresponding coefficients, and is the error value. We show that the
above formula is valid only for the finite values of . In other words, the condition 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.