Gauss-Radau Quadrature Rule Using Special Class of Polynomials.

A form of Gauss-Quadrature rule over [0,1] has been investigated that involves the derivative of the integrand at the pre-assigned left or right end node. This situation arises when the underlying polynomials are orthogonal with respect to the weight function (ω) := 1 - x over [0,1] . Along the lines of Golub's work, the nodes and weights of the quadrature rule are computed from a Jacobi-type matrix with entries related to simple rational sequences. The structure of these sequences is based on some characteristics of the identity-type polynomials recently developed by one of the authors. The devised rule has a slight advantage over that subject to the weight function (ω) := 1. [ABSTRACT FROM AUTHOR]