Properties of Generalized Freud Polynomials

Clarkson, Peter and Jordaan, Kerstin (2016) Properties of Generalized Freud Polynomials. Technical report. arxiv.org

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)
Subjects:	Q Science > QA Mathematics (inc Computing science) > QA351 Special functions Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions:	Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User:	Peter A Clarkson
Date Deposited:	18 Jan 2017 06:03 UTC
Last Modified:	29 May 2019 18:33 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/59905 (The current URI for this page, for reference purposes)
Clarkson, Peter:	https://orcid.org/0000-0002-8777-5284