Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type

Abstract

In the flrst part of this survey paper we present a short account on some impor- tant properties of orthogonal polynomials on the real line, including computational methods for constructing coe-cients in the fundamental three-term recurrence relation for orthogonal polynomials, and mention some basic facts on Gaussian quadrature rules. In the second part we discuss our Mathematica package OrthogonalPolynomials (see (2)) and show some ap- plications to problems with strong nonclassical weights on (0;+1), including a conjecture for an oscillatory weight on (i1;1). Finally, we give some new results on orthogonal polynomials on radial rays in the complex plane.