Clarkson, Peter and Jordaan, Kerstin (2016) Properties of Generalized Freud Polynomials. Technical report. arxiv.org (KAR id:59905)
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Official URL: https://arxiv.org/abs/1606.06026 |
Abstract
We consider the semi-classical generalized Freud weight function
w?(x;t)=|x|2?+1exp(?x4+tx2),x??,
with ?>?1 and t?? parameters. We analyze the asymptotic behavior of the sequences of monic polynomials that are orthogonal with respect to w?(x;t), as well as the asymptotic behavior of the recurrence coefficient, when the degree, or alternatively, the parameter t, tend to infinity. We also investigate existence and uniqueness of positive solutions of the nonlinear difference equation satisfied by the recurrence coefficients and prove properties of the zeros of the generalized Freud polynomials.
Item Type: | Monograph (Technical report) |
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Subjects: |
Q Science > QA Mathematics (inc Computing science) > QA351 Special functions Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations |
Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Depositing User: | Peter Clarkson |
Date Deposited: | 18 Jan 2017 06:03 UTC |
Last Modified: | 09 Dec 2022 03:22 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/59905 (The current URI for this page, for reference purposes) |
Clarkson, Peter: | ![]() |
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