On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials
The dual discrete q-ultraspherical polynomials Dn(s)(μ(x;s)|q) correspond to indeterminate moment problem and, therefore, have one-parameter family of extremal orthogonality relations. It is shown that special cases of dual discrete q-ultraspherical polynomials Dn(s)(μ(x;s)|q), when s = q⁻¹ and s =...
Збережено в:
| Дата: | 2006 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2006
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146429 |
| 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: | On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials / V.A. Groza, I.I. Kachuryk // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 11 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146429 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1464292019-02-10T01:24:21Z On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials Groza, V.A. Kachuryk, I.I. The dual discrete q-ultraspherical polynomials Dn(s)(μ(x;s)|q) correspond to indeterminate moment problem and, therefore, have one-parameter family of extremal orthogonality relations. It is shown that special cases of dual discrete q-ultraspherical polynomials Dn(s)(μ(x;s)|q), when s = q⁻¹ and s = q, are directly connected with q⁻¹-Hermite polynomials. These connections are given in an explicit form. Using these relations, all extremal orthogonality relations for these special cases of polynomials Dn(s)(μ(x;s)|q) are found. 2006 Article On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials / V.A. Groza, I.I. Kachuryk // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 11 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 33D45; 81Q99 http://dspace.nbuv.gov.ua/handle/123456789/146429 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 dual discrete q-ultraspherical polynomials Dn(s)(μ(x;s)|q) correspond to indeterminate moment problem and, therefore, have one-parameter family of extremal orthogonality relations. It is shown that special cases of dual discrete q-ultraspherical polynomials Dn(s)(μ(x;s)|q), when s = q⁻¹ and s = q, are directly connected with q⁻¹-Hermite polynomials. These connections are given in an explicit form. Using these relations, all extremal orthogonality relations for these special cases of polynomials Dn(s)(μ(x;s)|q) are found. |
| format |
Article |
| author |
Groza, V.A. Kachuryk, I.I. |
| spellingShingle |
Groza, V.A. Kachuryk, I.I. On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Groza, V.A. Kachuryk, I.I. |
| author_sort |
Groza, V.A. |
| title |
On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials |
| title_short |
On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials |
| title_full |
On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials |
| title_fullStr |
On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials |
| title_full_unstemmed |
On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials |
| title_sort |
on orthogonality relations for dual discrete q-ultraspherical polynomials |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146429 |
| citation_txt |
On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials / V.A. Groza, I.I. Kachuryk // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 11 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT grozava onorthogonalityrelationsfordualdiscretequltrasphericalpolynomials AT kachurykii onorthogonalityrelationsfordualdiscretequltrasphericalpolynomials |
| first_indexed |
2023-05-20T17:24:22Z |
| last_indexed |
2023-05-20T17:24:22Z |
| _version_ |
1796153218199191552 |