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Abstract: We prove a parametric generalization of the classical Poincare-Perron theoremon stabilizing recurrence relations where we assume that the varyingcoefficients of a recurrence depend on auxiliary parameters and convergeuniformly in these parameters to their limiting values. As an application westudy convergence of the ratios of families of functions satisfying finiterecurrence relations with varying functional coefficients. For example, weexplicitly describe the asymptotic ratio for sequences of biorthogonalpolynomials introduced by Ismail and Masson.



Author: J.Borcea, S.Friedland, B.Shapiro

Source: https://arxiv.org/



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