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Differential, difference, and asymptotic relations for Pollaczek–Jacobi type orthogonal polynomials and their Hankel determinants
Min, Chao1; Chen, Yang2
2021-07-01
Source PublicationStudies in Applied Mathematics
ISSN0022-2526
Volume147Issue:1Pages:390-416
Abstract

In this paper, we study the orthogonal polynomials with respect to a singularly perturbed Pollaczek–Jacobi type weight (Formula presented.) By using the ladder operator approach, we establish the second-order difference equations satisfied by the recurrence coefficient (Formula presented.) and the sub-leading coefficient (Formula presented.) of the monic orthogonal polynomials, respectively. We show that the logarithmic derivative of (Formula presented.) can be expressed in terms of a particular Painlevé V transcendent. The large (Formula presented.) asymptotic expansions of (Formula presented.) and (Formula presented.) are obtained by using Dyson's Coulomb fluid method together with the related difference equations. Furthermore, we study the associated Hankel determinant (Formula presented.) and show that a quantity (Formula presented.), allied to the logarithmic derivative of (Formula presented.), can be expressed in terms of the (Formula presented.) -function of a particular Painlevé V. The second-order differential and difference equations for (Formula presented.) are also obtained. In the end, we derive the large (Formula presented.) asymptotics of (Formula presented.) and (Formula presented.) from their relations with (Formula presented.) and (Formula presented.).

KeywordAsymptotic Expansions Hankel Determinant Ladder Operators Orthogonal Polynomials Painlevé v Pollaczek–jacobi Type Weight
DOI10.1111/sapm.12392
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000651112500001
Scopus ID2-s2.0-85105818752
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Cited Times [WOS]:4   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorMin, Chao
Affiliation1.School of Mathematical Sciences, Huaqiao University, Quanzhou, China
2.Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, China
Recommended Citation
GB/T 7714
Min, Chao,Chen, Yang. Differential, difference, and asymptotic relations for Pollaczek–Jacobi type orthogonal polynomials and their Hankel determinants[J]. Studies in Applied Mathematics,2021,147(1):390-416.
APA Min, Chao,&Chen, Yang.(2021).Differential, difference, and asymptotic relations for Pollaczek–Jacobi type orthogonal polynomials and their Hankel determinants.Studies in Applied Mathematics,147(1),390-416.
MLA Min, Chao,et al."Differential, difference, and asymptotic relations for Pollaczek–Jacobi type orthogonal polynomials and their Hankel determinants".Studies in Applied Mathematics 147.1(2021):390-416.
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