Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2015
• Main Authors: Dai, D., Hu, W., Wang, X.S.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2015
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147120
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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...