Some Indeterminate Moment Problems and Freud-Like Weights |
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| Authors: | Yang Chen M E H Ismail |
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| Institution: | (1) Department of Mathematics Imperial College 180 Queen's Gate London SW7 2BZ England y.chen@ic.ac.uk, UK;(2) Department of Mathematics University of South Florida Tampa Florida 33620-5700 U.S.A. ismail@math.usf.edu, US |
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| Abstract: | We study two indeterminate Hamburger moment problems and the corresponding orthogonal polynomials. The coefficients in their
recurrence relations are of exponential growth or are polynomials of degree 2. The entire functions in the Nevanlinna parametrization
are found. The orthogonal polynomials with polynomial recurrence coefficients resemble the Freud polynomials with a = 1/2 . Inequalities are given for the largest zero and the asymptotic behavior of the largest zero is established.
April 24, 1996. Date revised: March 3, 1997. |
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| Keywords: | , Moment problems, Freud weights, Recurrence relations, Nevanlinna parametrization, Zeros, Asymptotics, Inequalities,,,,,,AMS Classification, Primary 33D45, Secondary 30E05, |
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