On q-orthogonal polynomials, dual to little and big q-Jacobi polynomials
| dc.creator | Atakishiyev, N. M. | |
| dc.creator | Klimyk, A. U. | |
| dc.date | 2003-07-17 | |
| dc.date | 2003-10-06 | |
| dc.date.accessioned | 2026-07-07T04:59:45Z | |
| dc.date.available | 2026-07-07T04:59:45Z | |
| dc.description | This paper studies properties of q-Jacobi polynomials and their duals by means of operators of the discrete series representations for the quantum algebra U_q(su_{1,1}). Spectrum and eigenfunctions of these operators are found explicitly. These eigenfunctions, when normalized, form an orthogonal basis in the representation space. The initial U_q(su_{1,1})-basis and the bases of these eigenfunctions are interconnected by matrices, whose entries are expressed in terms of little and big q-Jacobi polynomials. The orthogonality by rows in these unitary connection matrices leads to the orthogonality relations for little and big q-Jacobi polynomials. The orthogonality by columns in the connection matrices leads to an explicit form of orthogonality relations on the countable set of points for {}_3ϕ_2 and {}_3ϕ_1 polynomials, which are dual to big and little q-Jacobi polynomials, respectively. The orthogonality measure for the dual little q-Jacobi polynomials proves to be extremal, whereas the measure for the dual big q-Jacobi polynomials is not extremal. | |
| dc.description | 26 pages, LaTeX, the exposition is slightly improved and some additional references have been added | |
| dc.identifier | https://arxiv.org/abs/math/0307250 | |
| dc.identifier | http://arxiv.org/abs/math/0307250 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68111 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Quantum Algebra | |
| dc.subject | 33D80, 33D45, 17B37 | |
| dc.title | On q-orthogonal polynomials, dual to little and big q-Jacobi polynomials | |
| dc.type | text |