UM  > Faculty of Science and Technology  > DEPARTMENT OF MATHEMATICS
Affiliated with RCfalse
Status已發表Published
A NOTE ON THE ASYMPTOTICS OF THE HANKEL DETERMINANT ASSOCIATED WITH TIME-DEPENDENT JACOBI POLYNOMIALS
Min, Chao1; Chen, Yang2
2022-04
Source PublicationProceedings of the American Mathematical Society
ISSN0002-9939
Volume150Issue:4Pages:1719-1728
Abstract

In 2010, Basor, Chen and Ehrhardt [J. Phys. A 43 (2010), 015204 (25 pp)] studied the (monic) time-dependent Jacobi polynomials. They proved that the diagonal recurrence coefficient α(t) satisfies a particular Painlevé V equation and the sub-leading coefficient p(n, t) satisfies the Jimbo-Miwa-Okamoto σ-form of Painlevé V under suitable transformations. In the end they made some conjectures about the large n asymptotics of the associated Hankel determinant. In this note we will derive the large n asymptotics of the Hankel determinant, together with the recurrence coefficients, the sub-leading coefficient and the square of L-norm of the time-dependent Jacobi polynomials. We will also show the relation between our problem and Heun’s differential equations.

KeywordHankel Determinant Heun’s Differential Equations Large n Asymptotics Painlevé v Recurrence Coefficients Time-dependent Jacobi Polynomials
DOI10.1090/proc/15887
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000768808400031
Scopus ID2-s2.0-85124612129
Fulltext Access
Citation statistics
Cited Times [WOS]:0   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorMin, Chao
Affiliation1.School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, China
2.Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao
Recommended Citation
GB/T 7714
Min, Chao,Chen, Yang. A NOTE ON THE ASYMPTOTICS OF THE HANKEL DETERMINANT ASSOCIATED WITH TIME-DEPENDENT JACOBI POLYNOMIALS[J]. Proceedings of the American Mathematical Society,2022,150(4):1719-1728.
APA Min, Chao,&Chen, Yang.(2022).A NOTE ON THE ASYMPTOTICS OF THE HANKEL DETERMINANT ASSOCIATED WITH TIME-DEPENDENT JACOBI POLYNOMIALS.Proceedings of the American Mathematical Society,150(4),1719-1728.
MLA Min, Chao,et al."A NOTE ON THE ASYMPTOTICS OF THE HANKEL DETERMINANT ASSOCIATED WITH TIME-DEPENDENT JACOBI POLYNOMIALS".Proceedings of the American Mathematical Society 150.4(2022):1719-1728.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Min, Chao]'s Articles
[Chen, Yang]'s Articles
Baidu academic
Similar articles in Baidu academic
[Min, Chao]'s Articles
[Chen, Yang]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Min, Chao]'s Articles
[Chen, Yang]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.