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

Abstract

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.