On the semi-classical character of orthogonal polynomials satisfying structure relations

We prove the semi-classical character of some sequences of orthogonal polynomials, say , , related through relations of the following type: , where denotes the monic polynomial associated with the pth order derivative of , and are complex numbers. The case is studied for a pair of orthogonal polynom...

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Bibliographic Details
Published inJournal of difference equations and applications Vol. 18; no. 1; pp. 111 - 138
Main Authors Branquinho, A., Rebocho, M. N.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis Group 01.01.2012
Taylor & Francis Ltd
Subjects
Coherence
Complex numbers
Derivatives
Difference equations
Differential equations
Mathematical analysis
orthogonal polynomials
Orthogonality
Polynomials
recurrence relations
semi-classical linear functionals
structure relations
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Summary:We prove the semi-classical character of some sequences of orthogonal polynomials, say , , related through relations of the following type: , where denotes the monic polynomial associated with the pth order derivative of , and are complex numbers. The case is studied for a pair of orthogonal polynomials whose corresponding orthogonality measures are coherent. The relation is shown to give a characterization for the semi-classical character of .
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1023-6198
1563-5120
DOI:10.1080/10236198.2010.529137