Asymptotics for solutions of systems of smooth recurrence equations

William Charles Bauldry, Attila Mate and Paul Nevai

Vol. 133 (1988), No. 2, 209–227

DOI: 10.2140/pjm.1988.133.209

Abstract

It is shown that convergent solutions of a system of smooth recurrence equations whose Jacobian matrix satisfies a certain “nonunimodularity” condition can be approximated by asymptotic expansions. An application is given to approximate the recurrence coefficients associated with polynomials orthonormal with respect to the weight exp(−Q(x)), where Q is an even degree polynomial with positive leading coefficients.

Mathematical Subject Classification 2000

Primary: 39A10

Secondary: 42C05, 33A65

Milestones

Received: 16 June 1986

Published: 1 June 1988