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 Affiliated with RC false Status 已發表Published 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 Publication Jaen Journal on Approximation ISSN 1889-3066 Volume 11Issue:1-2Pages:47-65 Abstract 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 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. Keyword Asymptotic expansions Backlund transformations Difference equations Orthogonal polynomials Painleveequations URL View the original Language 英語English Scopus ID 2-s2.0-85081716613 Fulltext Access Citation statistics Document Type Journal article Collection DEPARTMENT OF MATHEMATICS Affiliation 1.Department of Mathematics,University of Macau,Taipa, Macau,Av. Padre Tomas Pereiro,China2.University of Warsaw,Warsaw,Banacha 2,02-097,Poland3.Departamento de Matematica,Universidade da Beira Interior,Covilha,6201-001,Portugal4.CMUC,Department of Mathematics,University of Coimbra,Coimbra,Apartado 3008, EC Santa Cruz,3001-501,Portugal First Author Affilication University of Macau Recommended CitationGB/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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