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classical orthogonal polynomials of several variables

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2 - Orthogonal Polynomials of Several Variables
- By Yuan Xu
Edited by Tom H. Koornwinder, Universiteit van Amsterdam, Jasper V. Stokman, Universiteit van Amsterdam
Book:

Encyclopedia of Special Functions: The Askey-Bateman Project

Published online:

30 September 2020

Print publication:

15 October 2020, pp 19-78
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Summary

This chapter presents the theory of orthogonal polynomials in several variables. Serving as a reference to the subject, it provides modern treatment and results on the subject as well as historical references. It covers the general theory and emphasizes the classical type of orthogonal polynomials whose weight functions are supported on regular domains. Orthogonal polynomials of two variables are treated separately. The cases of continuous weight functions and of discrete weights are both discussed. Formulas of orthogonal polynomials and their structural constraints are given explicitly whenever feasible.