Report
Asymptotics of Discrete $q$-Freud $\mathrm{II}$ orthogonal polynomials from the $q$-Riemann Hilbert Problem
| العنوان: | Asymptotics of Discrete $q$-Freud $\mathrm{II}$ orthogonal polynomials from the $q$-Riemann Hilbert Problem |
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| المؤلفون: | Joshi, Nalini, Latimer, Tomas Lasic |
| المصدر: | Nonlinearity 36.3969 (2023) |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Classical Analysis and ODEs, Mathematical Physics |
| الوصف: | We investigate a Riemann-Hilbert problem (RHP), whose solution corresponds to a group of $q$-orthogonal polynomials studied earlier by Ismail et al. Using RHP theory we determine new asymptotic results in the limit as the degree of the polynomials approach infinity. The RHP formulation also enables us to obtain further properties. In particular, we consider how the class of polynomials and their asymptotic behaviours change under translations of the $q$-discrete lattice and determine the asymptotics of related $q$-Painlev\'e equations. Comment: 33 pages, no figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1088/1361-6544/acdbb3 |
| URL الوصول: | http://arxiv.org/abs/2211.12658 |
| رقم الانضمام: | edsarx.2211.12658 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1088/1361-6544/acdbb3 |
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