Complex versus real orthogonal polynomials of two variables

Orthogonal polynomials of two real variables can often be represented in complex variables. We explore the connection between the two types of representations and study the structural relations of complex orthogonal polynomials. The complex Hermite orthogonal polynomials and the disk polynomials are...

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Bibliographic Details
Published in:Integral transforms and special functions Vol. 26; no. 2; pp. 134 - 151
Main Author: Xu, Yuan
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 01.02.2015
Taylor & Francis Ltd
Subjects:
complex Hermite
complex orthogonal polynomials
Complex variables
disk polynomials
Disks
Functions (mathematics)
Hermite polynomials
Joints
Mathematical analysis
orthogonal polynomials of two variables
Polynomials
Representations
several variables
ISSN:1065-2469, 1476-8291
Online Access:Get full text
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Summary:Orthogonal polynomials of two real variables can often be represented in complex variables. We explore the connection between the two types of representations and study the structural relations of complex orthogonal polynomials. The complex Hermite orthogonal polynomials and the disk polynomials are used as illustrating examples.
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ISSN:1065-2469
1476-8291
DOI:10.1080/10652469.2014.973196