Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States
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| Creator |
Dai, D.
Hu, W. Wang, X.S. |
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| Description |
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.
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| Date |
2019-02-13T17:00:06Z
2019-02-13T17:00:06Z 2015 |
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| Type |
Article
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| Identifier |
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.
1815-0659 2010 Mathematics Subject Classification: 41A60; 33C45 DOI:10.3842/SIGMA.2015.070 http://dspace.nbuv.gov.ua/handle/123456789/147120 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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