تقرير
Small $x$ asymptotics for special function solutions of Painlev\'e III equation
| العنوان: | Small $x$ asymptotics for special function solutions of Painlev\'e III equation |
|---|---|
| المؤلفون: | Pan, Hao, Prokhorov, Andrei |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics Nonlinear Sciences |
| مصطلحات موضوعية: | Mathematics - Classical Analysis and ODEs, Mathematical Physics, Mathematics - Complex Variables, Nonlinear Sciences - Exactly Solvable and Integrable Systems, 33C10, 33E17, 34E05, 34M55, 34M56 |
| الوصف: | In this paper we compute the small $x$ asymptotics of the special function solutions of Painlev\'e-III equation. We use the representation of solution in terms of Hankel determinants of Bessel functions, which seems to be new. Hankel determinants can be rewritten as multiple contour integrals using Andr\`eief identity. Finally small $x$ asymptotics is obtained using elementary asymptotic methods. Comment: 25 pages, 7 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.04852 |
| رقم الأكسشن: | edsarx.2407.04852 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |