Asymptotics for solutions of systems of smooth recurrence equations
William C. Bauldry, Attila Máté, Paul Nevai · Pacific Journal of Mathematics · 1988
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(-β(x)), where Q is an even degree polynomial with positive leading coefficients.