Orthogonal Polynomials On Ellipses And Their Recurrence Relations

Abstract

In this note we study the connection between orthogonal polynomials on an ellipse and orthogonal Laurent polynomials on the unit circle relative to some multiplicative measures and then establish the recurrence relations for orthogonal polynomials on an ellipse. The matrix representation of the operator of multiplication by coordinate function is obtained

Keywords

• orthogonal polynomials on ellipses
• recurrence relations
• Hessenberg matrix