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Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States
Інший ID:
2010 Mathematics Subject Classification: 41A60; 33C45
DOI:10.3842/SIGMA.2015.070
DOI:10.3842/SIGMA.2015.070
Посилання:
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.
Підтримка:
We are grateful to Professor Mourad Ismail for his helpful comments and discussions. We
would also like to thank the anonymous referees for their constructive suggestions which lead to
a significant improvement of the manuscript.
DD and WH were partially supported by grants from the Research Grants Council of the Hong
Kong Special Administrative Region, China (Project No. CityU 101411, CityU 11300814). In addition, DD was partially supported by a grant from the City University of Hong Kong (Project
No. 7004065). XSW was partially supported by two grants (Start-up Fund and Summer Research
Grant) from Southeast Missouri State University.
Дата:
2015
Переглядів:
562
Завантажень:
257
Анотація:
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 suggest that the weight function associated with the polynomials has an unusual singularity, which has never appeared for orthogonal polynomials in the Askey scheme. Our main technique is the Wang and Wong's difference equation method. In addition, the limiting zero distribution of the polynomials ϕn(z) is provided.
