Asymptotics of the coefficients of polynomials, asymptotic zero distribution and free probability
Walter Van Assche
Abstract
The asymptotic behavior of the coefficients of a sequence of polynomials is given under the conditions that all the zeros are real and positive and the zeros have an asymptotic zero distribution on (0,∞). We show how the limit for the coefficients is related to the Stieltjes transform of the asymptotic zero distribution and make a connection with the S-transform in free probability. We illustrate with some examples involving orthogonal and multiple orthogonal polynomials.
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