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Nonlinear difference equations for a modified laguerre weight: Laguerre-freud equations and asymptotics
Chen,Yang1; Filipuk,Galina2; das Neves Rebocho,Maria3,4
2019-12-01
Source PublicationJaen Journal on Approximation
ISSN1889-3066
Volume11Issue:1-2Pages:47-65
AbstractIn this paper we derive second and third order nonlinear difference equations for one of the recurrence coefficients in the three term recurrence relation of polyno¬mials orthogonal with respect to a modified Laguerre weight. We show how these equations can be obtained from the Backlund transformations of the third Painleve 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.
KeywordAsymptotic expansions Backlund transformations Difference equations Orthogonal polynomials Painleveequations
URLView the original
Language英語English
Scopus ID2-s2.0-85081716613
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Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Department of Mathematics,University of Macau,Taipa, Macau,Av. Padre Tomas Pereiro,China
2.University of Warsaw,Warsaw,Banacha 2,02-097,Poland
3.Departamento de Matematica,Universidade da Beira Interior,Covilha,6201-001,Portugal
4.CMUC,Department of Mathematics,University of Coimbra,Coimbra,Apartado 3008, EC Santa Cruz,3001-501,Portugal
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Chen,Yang,Filipuk,Galina,das Neves Rebocho,Maria. Nonlinear difference equations for a modified laguerre weight: Laguerre-freud equations and asymptotics[J]. Jaen Journal on Approximation,2019,11(1-2):47-65.
APA Chen,Yang,Filipuk,Galina,&das Neves Rebocho,Maria.(2019).Nonlinear difference equations for a modified laguerre weight: Laguerre-freud equations and asymptotics.Jaen Journal on Approximation,11(1-2),47-65.
MLA Chen,Yang,et al."Nonlinear difference equations for a modified laguerre weight: Laguerre-freud equations and asymptotics".Jaen Journal on Approximation 11.1-2(2019):47-65.
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