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 =...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2006 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2006
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146429 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862560807805517824 |
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| author | Groza, V.A. Kachuryk, I.I. |
| author_facet | Groza, V.A. Kachuryk, I.I. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-25T23:08:41Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146429 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T23:08:41Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Groza, V.A. Kachuryk, I.I. 2019-02-09T16:53:59Z 2019-02-09T16:53:59Z 2006 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 https://nasplib.isofts.kiev.ua/handle/123456789/146429 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials Article published earlier |
| spellingShingle | On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials Groza, V.A. Kachuryk, I.I. |
| title | 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_short | On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials |
| title_sort | on orthogonality relations for dual discrete q-ultraspherical polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146429 |
| work_keys_str_mv | AT grozava onorthogonalityrelationsfordualdiscretequltrasphericalpolynomials AT kachurykii onorthogonalityrelationsfordualdiscretequltrasphericalpolynomials |