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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| Datum: | 2006 |
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| Sprache: | English |
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Інститут математики НАН України
2006
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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nasplib_isofts_kiev_ua-123456789-1464292025-02-09T12:13:33Z 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 https://nasplib.isofts.kiev.ua/handle/123456789/146429 en Symmetry, Integrability and Geometry: Methods and Applications application/pdf 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 |
https://nasplib.isofts.kiev.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 |
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2025-11-25T23:08:41Z |
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2025-11-25T23:08:41Z |
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1849805631627722752 |