On the orthogonality measure of the q-pollaczek polynomials
The q-Pollaczek polynomials F ,(x) depend on four parameters u,v, ∆, q and are given by the recurrence relation (1-qn+1)Fn+1(x) = 2[(1-u∆qn)x+vqn]Fn(x)- (1-∆2qn-1)Fn-1 (x), n ≥ 1, and the initial cond i t i ons Fo(x)=1 F1(x) = 2 [(1-u∆)x+v]/1-q. The measure with respect to which the Fn(x)'s are...
- Autores:
-
Charris Castañeda, Jairo Antonio
Gómez, Luis A.
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 1987
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/43171
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/43171
http://bdigital.unal.edu.co/33269/
- Palabra clave:
- q-Pollaczek polynomials
orthogonal
Lebesgue's measure
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | The q-Pollaczek polynomials F ,(x) depend on four parameters u,v, ∆, q and are given by the recurrence relation (1-qn+1)Fn+1(x) = 2[(1-u∆qn)x+vqn]Fn(x)- (1-∆2qn-1)Fn-1 (x), n ≥ 1, and the initial cond i t i ons Fo(x)=1 F1(x) = 2 [(1-u∆)x+v]/1-q. The measure with respect to which the Fn(x)'s are orthogonal is determined when the parameters are subject to the constraints O and lt;u and lt;∆ and lt; 1, ∆(1-u) and gt;±v, 0 and lt; q and lt; 1. This measure turns out to be absolutelv continuous with respect to Lebesgue's measure. |
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