On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials
The dual discrete $q$-ultraspherical polynomials $D_n^{(s)}(mu (x;s)|q)$ 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 $D_n^{(s)}(mu (x;s)|q)$, w...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2006-03-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://www.emis.de/journals/SIGMA/2006/Paper034/ |
| Summary: | The dual discrete $q$-ultraspherical polynomials $D_n^{(s)}(mu (x;s)|q)$ 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 $D_n^{(s)}(mu (x;s)|q)$, 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 $D_n^{(s)}(mu (x;s)|q)$ are found. |
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| ISSN: | 1815-0659 |