Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States
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...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2015 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2015
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147120 |
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| 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862564516153262080 |
|---|---|
| author | Dai, D. Hu, W. Wang, X.S. |
| author_facet | Dai, D. Hu, W. Wang, X.S. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-11-25T23:46:46Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147120 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T23:46:46Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Dai, D. Hu, W. Wang, X.S. 2019-02-13T17:00:06Z 2019-02-13T17:00:06Z 2015 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 https://nasplib.isofts.kiev.ua/handle/123456789/147120 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States Article published earlier |
| spellingShingle | Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States Dai, D. Hu, W. Wang, X.S. |
| title | Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States |
| title_full | Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States |
| title_fullStr | Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States |
| title_full_unstemmed | Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States |
| title_short | Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States |
| title_sort | uniform asymptotics of orthogonal polynomials arising from coherent states |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147120 |
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