Q-classical orthogonal polynomials: a very classical approach
The q-classical orthogonal polynomials defined by Hahn satisfy a Sturm-Liouville type equation in geometric differences. Working with this, we classify the q−classical polynomials in twelve families according to the zeros of the polynomial coefficients of the equation and the behavior concerning to...
| Autores: | ; |
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| Tipo de documento: | Artigo |
| Estado: | Published version |
| Data de publicação: | 1999 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositório: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/49288 |
| Acesso em linha: | http://hdl.handle.net/11441/49288 |
| Nível de acesso: | Acesso aberto |
| Palavra-chave: | Orthogonal q-polynomials Classical polynomials |
| Resumo: | The q-classical orthogonal polynomials defined by Hahn satisfy a Sturm-Liouville type equation in geometric differences. Working with this, we classify the q−classical polynomials in twelve families according to the zeros of the polynomial coefficients of the equation and the behavior concerning to q-1. We determine a q-analogue of the weight function for the twelve families, and we give a representation of its orthogonality relation and its q-integral. We describe this representation in some normal and special cases (indeterminate moment problem and finite orthogonal sequences). Finally, the Sturm-Liouville type equation allows us to establish the correspondence between this classification and the Askey Scheme. |
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