Article
Q-classical orthogonal polynomials: a very classical approach
Author/s | Marcellán Español, Francisco
Medem Roesicke, Juan Carlos |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 1999 |
Deposit Date | 2016-11-29 |
Published in |
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Abstract | 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 ... 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. |
Funding agencies | Dirección General de Enseñanza Superior. España |
Project ID. | PB-96-0120-C03-01 |
Citation | Marcellán Español, F. y Medem Roesicke, J.C. (1999). Q-classical orthogonal polynomials: a very classical approach. Electronic Transactions on Numerical Analysis, 9, 112-127. |
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