Orthogonal Basic Hypergeometric Laurent Polynomials
The Askey-Wilson polynomials are orthogonal polynomials in x=cosθ, which are given as a terminating ₄∅₃ basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in z=eiθ, which are given as a sum of two terminating ₄∅₃'s. They satisfy a biorthogonality rel...
Збережено в:
| Дата: | 2012 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148664 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Orthogonal Basic Hypergeometric Laurent Polynomials / Mourad E.H. Ismail, D. Stanton // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 21 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148664 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1486642019-02-19T01:28:06Z Orthogonal Basic Hypergeometric Laurent Polynomials Mourad E.H. Ismail Stanton, D. The Askey-Wilson polynomials are orthogonal polynomials in x=cosθ, which are given as a terminating ₄∅₃ basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in z=eiθ, which are given as a sum of two terminating ₄∅₃'s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single ₄∅₃'s which are Laurent polynomials in z are given, which imply the non-symmetric Askey-Wilson biorthogonality. These results include discrete orthogonality relations. They can be considered as a classical analytic study of the results for non-symmetric Askey-Wilson polynomials which were previously obtained by affine Hecke algebra techniques. 2012 Article Orthogonal Basic Hypergeometric Laurent Polynomials / Mourad E.H. Ismail, D. Stanton // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 21 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33D45 DOI: http://dx.doi.org/10.3842/SIGMA.2012.092 http://dspace.nbuv.gov.ua/handle/123456789/148664 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 |
The Askey-Wilson polynomials are orthogonal polynomials in x=cosθ, which are given as a terminating ₄∅₃ basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in z=eiθ, which are given as a sum of two terminating ₄∅₃'s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single ₄∅₃'s which are Laurent polynomials in z are given, which imply the non-symmetric Askey-Wilson biorthogonality. These results include discrete orthogonality relations. They can be considered as a classical analytic study of the results for non-symmetric Askey-Wilson polynomials which were previously obtained by affine Hecke algebra techniques. |
| format |
Article |
| author |
Mourad E.H. Ismail Stanton, D. |
| spellingShingle |
Mourad E.H. Ismail Stanton, D. Orthogonal Basic Hypergeometric Laurent Polynomials Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Mourad E.H. Ismail Stanton, D. |
| author_sort |
Mourad E.H. Ismail |
| title |
Orthogonal Basic Hypergeometric Laurent Polynomials |
| title_short |
Orthogonal Basic Hypergeometric Laurent Polynomials |
| title_full |
Orthogonal Basic Hypergeometric Laurent Polynomials |
| title_fullStr |
Orthogonal Basic Hypergeometric Laurent Polynomials |
| title_full_unstemmed |
Orthogonal Basic Hypergeometric Laurent Polynomials |
| title_sort |
orthogonal basic hypergeometric laurent polynomials |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148664 |
| citation_txt |
Orthogonal Basic Hypergeometric Laurent Polynomials / Mourad E.H. Ismail, D. Stanton // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 21 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT mouradehismail orthogonalbasichypergeometriclaurentpolynomials AT stantond orthogonalbasichypergeometriclaurentpolynomials |
| first_indexed |
2023-05-20T17:31:11Z |
| last_indexed |
2023-05-20T17:31:11Z |
| _version_ |
1796153472038469632 |