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(-(x)), where Q is an even degree polynomial with positive leading coefficients.
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Bauldry et al. (1988) studied this question.