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Orientador(es)
Resumo(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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Descrição
Palavras-chave
Orthogonal polynomials Difference equations Painlev e equations Backlund transformations Asymptotic expansions
Contexto Educativo
Citação
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.