Affiliated with RC | false |
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 Publication | Proceedings of the American Mathematical Society |
ISSN | 0002-9939 |
Volume | 150Issue: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. |
Keyword | Hankel Determinant Heun’s Differential Equations Large n Asymptotics Painlevé v Recurrence Coefficients Time-dependent Jacobi Polynomials |
DOI | 10.1090/proc/15887 |
URL | View the original |
Indexed By | SCIE |
Language | 英語English |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000768808400031 |
Scopus ID | 2-s2.0-85124612129 |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | DEPARTMENT OF MATHEMATICS |
Corresponding Author | Min, Chao |
Affiliation | 1.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. |
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