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Laguerre–Freud equations associated with the D-Laguerre–Hahn forms of class one

Laguerre–Freud equations associated with the D-Laguerre–Hahn forms of class one AbstractWe give the system of Laguerre–Freud equations for the recurrence coefficients βn{\beta_{n}}, γn+1{\gamma_{n+1}}, n≥0{n\geq 0}, of orthogonal polynomials with respect to a D-Laguerre–Hahn form (linear functional) of class one. The system is solved in the case when β0=-θ0{\beta_{0}=-\theta_{0}}, βn+1=θn-θn+1{\beta_{n+1}=\theta_{n}-\theta_{n+1}} and γn+1=-θn2{\gamma_{n+1}=-\theta_{n}^{2}} with θn≠0{\theta_{n}\neq 0}, n≥0{n\geq 0}. There are essentially three canonical cases. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Pure and Applied Mathematics de Gruyter

Laguerre–Freud equations associated with the D-Laguerre–Hahn forms of class one

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Publisher
de Gruyter
Copyright
© 2019 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6090
eISSN
1869-6090
DOI
10.1515/apam-2018-0015
Publisher site
See Article on Publisher Site

Abstract

AbstractWe give the system of Laguerre–Freud equations for the recurrence coefficients βn{\beta_{n}}, γn+1{\gamma_{n+1}}, n≥0{n\geq 0}, of orthogonal polynomials with respect to a D-Laguerre–Hahn form (linear functional) of class one. The system is solved in the case when β0=-θ0{\beta_{0}=-\theta_{0}}, βn+1=θn-θn+1{\beta_{n+1}=\theta_{n}-\theta_{n+1}} and γn+1=-θn2{\gamma_{n+1}=-\theta_{n}^{2}} with θn≠0{\theta_{n}\neq 0}, n≥0{n\geq 0}. There are essentially three canonical cases.

Journal

Advances in Pure and Applied Mathematicsde Gruyter

Published: Oct 1, 2019

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