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Nonlinear difference equations arising from the generalized Stieltjes‐Wigert and q‐Laguerre weights
Hongmei Chen1; Galina Filipuk2; Yang Chen1
2018-04
Source PublicationMathematical Methods in the Applied Sciences
ISSN0170-4214
Volume41Issue:6Pages:2442–2465
Other Abstract

In this paper, we investigate the generalized Stieltjes‐Wigert and q‐Laguerre polynomials. We derive the second‐ and the third‐order nonlinear difference equations for the subleading coefficients of these polynomials and use them to find a few terms of the formal expansions in powers of qn/2. We also show how the recurrence coefficients in the three‐term recurrence relation for these polynomials can be computed efficiently by using the nonlinear difference equations for the subleading coefficient. Moreover, we obtain systems of difference equations with one of the equations being q‐discrete Painlevé III or V equations and analyze them by a singularity confinement. We also discuss certain generalized weights.

KeywordAsymptotic Expansions Singularity Confinement Difference Equations Discrete Painlevé Equations Orthogonal Polynomials
DOIhttps://doi.org/10.1002/mma.4751
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000427585700019
PublisherWILEY, 111 RIVER ST, HOBOKEN 07030-5774, NJ USA
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Document TypeJournal article
专题DEPARTMENT OF MATHEMATICS
Corresponding AuthorHongmei Chen
Affiliation1.Faculty of Science and Technology,Department of Mathematics, University ofMacau, Av. Padre Tomás Pereiro Taipa,Macau, China
2.Faculty of Mathematics, Informatics andMechanics, University of Warsaw,Banacha 2 Warsaw, 02-097, Poland
First Author AffilicationFaculty of Science and Technology
Corresponding Author AffilicationFaculty of Science and Technology
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Hongmei Chen,Galina Filipuk,Yang Chen. Nonlinear difference equations arising from the generalized Stieltjes‐Wigert and q‐Laguerre weights[J]. Mathematical Methods in the Applied Sciences,2018,41(6):2442–2465.
APA Hongmei Chen,Galina Filipuk,&Yang Chen.(2018).Nonlinear difference equations arising from the generalized Stieltjes‐Wigert and q‐Laguerre weights.Mathematical Methods in the Applied Sciences,41(6),2442–2465.
MLA Hongmei Chen,et al."Nonlinear difference equations arising from the generalized Stieltjes‐Wigert and q‐Laguerre weights".Mathematical Methods in the Applied Sciences 41.6(2018):2442–2465.
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