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Q-classical orthogonal polynomials: a very classical approach

 

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Author: Marcellán Español, Francisco
Medem Roesicke, Juan Carlos
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 1999
Published in: Electronic Transactions on Numerical Analysis, 9, 112-127.
Document type: Article
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 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.
Cite: 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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URI: http://hdl.handle.net/11441/49288

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