On quasi-orthogonal polynomials of order r

The sequences of quasi-orthogonal polynomials of order r are defined for non-quasi-definite moment functionals. Properties concerning the existence of such sequences, and relations between a quasi-orthogonal polynomial of order r and a set of orthogonal polynomials are proved. Two determinantal expr...

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Published inIntegral transforms and special functions Vol. 27; no. 9; pp. 747 - 765
Main Author Draux, A.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 01.09.2016
Taylor & Francis Ltd
Subjects
determinantal expression
Functionals
Functions (mathematics)
Integrals
Mathematical analysis
Mathematics
non-quasi-definite moment functional
Numerical Analysis
Polynomials
Quasi-orthogonal polynomial
Sequences
three term recurrence relation
Transforms
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Abstract The sequences of quasi-orthogonal polynomials of order r are defined for non-quasi-definite moment functionals. Properties concerning the existence of such sequences, and relations between a quasi-orthogonal polynomial of order r and a set of orthogonal polynomials are proved. Two determinantal expressions of quasi-orthogonal polynomials of order r are given. At last it is proved that three consecutive polynomials of a sequence of quasi-orthogonal polynomials of order r satisfy a three term recurrence relation.
AbstractList The sequences of quasi-orthogonal polynomials of order r are defined for non-quasi-definite moment functionals. Properties concerning the existence of such sequences, and relations between a quasi-orthogonal polynomial of order r and a set of orthogonal polynomials are proved. Two determinantal expressions of quasi-orthogonal polynomials of order r are given. At last it is proved that three consecutive polynomials of a sequence of quasi-orthogonal polynomials of order r satisfy a three term recurrence relation.
Author Draux, A.
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Cites_doi 10.1007/BF01385881
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2016 Informa UK Limited, trading as Taylor & Francis Group
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Snippet The sequences of quasi-orthogonal polynomials of order r are defined for non-quasi-definite moment functionals. Properties concerning the existence of such...
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SubjectTerms determinantal expression
Functionals
Functions (mathematics)
Integrals
Mathematical analysis
Mathematics
non-quasi-definite moment functional
Numerical Analysis
Polynomials
Quasi-orthogonal polynomial
Sequences
three term recurrence relation
Transforms
Title On quasi-orthogonal polynomials of order r
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