Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2015
• Автори: Dai, D., Hu, W., Wang, X.S.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2015
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/147120
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States / D. Dai, W. Hu, X.S. Wang // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 31 назв. — англ.

In this paper, we study a family of orthogonal polynomials {ϕn(z)} arising from nonlinear coherent states in quantum optics. Based on the three-term recurrence relation only, we obtain a uniform asymptotic expansion of ϕn(z) as the polynomial degree n tends to infinity. Our asymptotic results sugges...