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Exceptional solutions to the Painlevé VI equation associated with the generalized Jacobi weight
Lyu S.; Chen Y.
2017
Source PublicationRandom Matrices: Theory and Application
ISSN20103271 20103263
Volume6Issue:1
Abstract

We consider the generalized Jacobi weight x(1 - x)|x - t|, x ∈ [0, 1], t(t - 1) > 0, α > -1, β > -1, γ ∈ ℝ. As is shown in [D. Dai and L. Zhang, Painlevé VI and Henkel determinants for the generalized Jocobi weight, J. Phys. A: Math. Theor. 43 (2010), Article ID:055207, 14pp.], the corresponding Hankel determinant is the τ-function of a particular Painlevé VI. We present all the possible asymptotic expansions of the solution of the Painlevé VI equation near 0,∞ and 1 for generic (α,β,γ). For four special cases of (α,β,γ) which are related to the dimension of the Hankel determinant, we can find the exceptional solutions of the Painlevé VI equation according to the results of [A. Eremenko, A. Gabrielov and A. Hinkkanen, Exceptional solutions to the Painlevé VI equation, preprint (2016), arXiv:1602.04694], and thus give another characterization of the Hankel determinant.

KeywordAsymptotic Expansions Hankel Determinants Painléve Equations
DOIhttp://doi.org/10.1142/S2010326317500034
URLView the original
Indexed BySCI
Language英语
WOS Research AreaPhysics ; Mathematics
WOS SubjectPhysics, Mathematical ; Statistics & Probability
WOS IDWOS:000395372300004
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Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
AffiliationDepartment of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, P. R. China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Lyu S.,Chen Y.. Exceptional solutions to the Painlevé VI equation associated with the generalized Jacobi weight[J]. Random Matrices: Theory and Application,2017,6(1).
APA Lyu S.,&Chen Y..(2017).Exceptional solutions to the Painlevé VI equation associated with the generalized Jacobi weight.Random Matrices: Theory and Application,6(1).
MLA Lyu S.,et al."Exceptional solutions to the Painlevé VI equation associated with the generalized Jacobi weight".Random Matrices: Theory and Application 6.1(2017).
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