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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| Дата: | 2015 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
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irk-123456789-1471202019-02-14T01:25:42Z Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States Dai, D. Hu, W. Wang, X.S. 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. 2015 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Dai, D. Hu, W. Wang, X.S. |
| spellingShingle |
Dai, D. Hu, W. Wang, X.S. Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Dai, D. Hu, W. Wang, X.S. |
| author_sort |
Dai, D. |
| title |
Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States |
| title_short |
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_sort |
uniform asymptotics of orthogonal polynomials arising from coherent states |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147120 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:26:38Z |
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