Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptotics

Rebocho, M. N.; Filipuk, Galina; Chen, Yang

http://hdl.handle.net/10400.6/8992

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Authors

Rebocho, M. N.

Filipuk, Galina

Chen, Yang

Abstract(s)

In this paper we derive second and third order nonlinear difference equations for one of the recurrence coefficients in the three term recurrence relation of polynomials orthogonal with respect to a modified Laguerre weight. We show how these equations can be obtained from the Backlund transformations of the third Painlevé equation. We also show how to use nonlinear difference equations to derive a few terms in the formal asymptotic expansions in n of the recurrence coefficients.

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Keywords

Orthogonal polynomials Difference equations Painlev e equations Backlund transformations Asymptotic expansions

URI

http://hdl.handle.net/10400.6/8992

Citation

Y. Chen, G. Filipuk, and M.N. Rebocho, Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptotics, Jaen Journal on Approximation 11, no. 1-2 (2019) 47-65.