Bulletin of the Belgian Mathematical Society - Simon Stevin

The product of a regular form by a polynomial generalized: the case $xu=\lambda x^2v$

O.F. Kamech and M. Mejri

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Abstract

We consider the problem: given a regular form (linear functional) $v$, find all the regular forms $u$ which satisfy the relation $xu=\lambda x^2v,\lambda \in\C -\{0\}$. We give the second-order recurrence relation of the orthogonal polynomial sequence with respect to $u$. Some examples are studied.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 15, Number 2 (2008), 311-334.

Dates
First available in Project Euclid: 8 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1210254828

Digital Object Identifier
doi:10.36045/bbms/1210254828

Mathematical Reviews number (MathSciNet)
MR2424116

Zentralblatt MATH identifier
1149.42017

Subjects
Primary: 42C05: Orthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45] 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]

Keywords
Orthogonal polynomials quasi-definite forms

Citation

Kamech, O.F.; Mejri, M. The product of a regular form by a polynomial generalized: the case $xu=\lambda x^2v$. Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 2, 311--334. doi:10.36045/bbms/1210254828. https://projecteuclid.org/euclid.bbms/1210254828


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