A new class of orthogonal polynomials

A New Class of Orthogonal Polynomials on the Unit Circle

Even though the theory of orthogonal polynomials on the unit circle, also known as the theory of Szegő polynomials, is very extensive, it is less known than the theory of orthogonal polynomials on the real line. One reason for this may be that “beautiful” examples on the theory of Szegő polynomials are scarce. This is in contrast to the wonderful examples of Jacobi, Laguerrer and Hermite polyno...

A New Algorithm for Computing Orthogonal Polynomials

The aim of this paper is to present an algorithm for computing orthogonal polynomials. The Fast Fourier Transform completes the connection given by Draux between the three-term recurrence relationship and the Euclidian algorithm. Applications to Hankel systems and numerical examples illustrate our purpose.

A Non-standard Class of Sobolev Orthogonal Polynomials

When τ is a quasi-definite moment functional onP , the vector space of all real polynomials, we consider a symmetric bilinear form φ(·, ·) on P ×P defined by φ(p, q) = λp(a)q(a)+ μp(b)q(b)+ 〈τ, p′q ′〉, where λ,μ, a, and b are real numbers. We first find a necessary and sufficient condition for φ(·, ·) to be quasi-definite. When τ is a semi-classical moment functional, we discuss algebraic prope...

A New Class of Orthogonal Polynomials1

A new class of orthogonal polynomials is introduced which generalizes the Bernstein-Szegö polynomials and includes the associated polynomials as well. The purpose of this paper is to give a natural extension of the Bernstein-Szegö orthogonal polynomials for a general class of weight functions. A nonnegative function w defined on the real line is called a weight function if w > 0, fRw > 0 and al...

Generating New Classes of Orthogonal Polynomials