Recurrence Coefficients of a New Generalization of the Meixner Polynomials
We investigate new generalizations of the Meixner polynomials on the lattice N, on the shifted lattice N+1−β and on the bi-lattice N∪(N+1−β). We show that the coefficients of the three-term recurrence relation for the orthogonal polynomials are related to the solutions of the fifth Painlevé equation...
Збережено в:
| Дата: | 2011 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147388 |
| 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: | Recurrence Coefficients of a New Generalization of the Meixner Polynomials / G. Filipuk, W. Van Assche // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 12 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147388 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1473882019-02-15T01:22:59Z Recurrence Coefficients of a New Generalization of the Meixner Polynomials Filipuk, G. Van Assche, W. We investigate new generalizations of the Meixner polynomials on the lattice N, on the shifted lattice N+1−β and on the bi-lattice N∪(N+1−β). We show that the coefficients of the three-term recurrence relation for the orthogonal polynomials are related to the solutions of the fifth Painlevé equation PV. Initial conditions for different lattices can be transformed to the classical solutions of PV with special values of the parameters. We also study one property of the Bäcklund transformation of PV. 2011 Article Recurrence Coefficients of a New Generalization of the Meixner Polynomials / G. Filipuk, W. Van Assche // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 12 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34M55; 33E17; 33C47; 42C05; 64Q30 DOI:10.3842/SIGMA.2011.068 http://dspace.nbuv.gov.ua/handle/123456789/147388 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 |
We investigate new generalizations of the Meixner polynomials on the lattice N, on the shifted lattice N+1−β and on the bi-lattice N∪(N+1−β). We show that the coefficients of the three-term recurrence relation for the orthogonal polynomials are related to the solutions of the fifth Painlevé equation PV. Initial conditions for different lattices can be transformed to the classical solutions of PV with special values of the parameters. We also study one property of the Bäcklund transformation of PV. |
| format |
Article |
| author |
Filipuk, G. Van Assche, W. |
| spellingShingle |
Filipuk, G. Van Assche, W. Recurrence Coefficients of a New Generalization of the Meixner Polynomials Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Filipuk, G. Van Assche, W. |
| author_sort |
Filipuk, G. |
| title |
Recurrence Coefficients of a New Generalization of the Meixner Polynomials |
| title_short |
Recurrence Coefficients of a New Generalization of the Meixner Polynomials |
| title_full |
Recurrence Coefficients of a New Generalization of the Meixner Polynomials |
| title_fullStr |
Recurrence Coefficients of a New Generalization of the Meixner Polynomials |
| title_full_unstemmed |
Recurrence Coefficients of a New Generalization of the Meixner Polynomials |
| title_sort |
recurrence coefficients of a new generalization of the meixner polynomials |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147388 |
| citation_txt |
Recurrence Coefficients of a New Generalization of the Meixner Polynomials / G. Filipuk, W. Van Assche // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 12 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT filipukg recurrencecoefficientsofanewgeneralizationofthemeixnerpolynomials AT vanasschew recurrencecoefficientsofanewgeneralizationofthemeixnerpolynomials |
| first_indexed |
2023-05-20T17:27:19Z |
| last_indexed |
2023-05-20T17:27:19Z |
| _version_ |
1796153330727124992 |