scholarly journals Bi-orthogonal Polynomials on the Unit Circle, Regular Semi-Classical Weights and Integrable Systems

2006 ◽  
Vol 24 (2) ◽  
pp. 201-237 ◽  
Author(s):  
P.J. Forrester ◽  
N.S. Witte
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Integrable Systems

Multiple Orthogonal Polynomials on the Unit Circle

2007 ◽  
Vol 28 (2) ◽  
pp. 173-197 ◽  
Author(s):  
Judit Minguez Ceniceros ◽  
Walter Van Assche
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Multiple Orthogonal Polynomials

scholarly journals Mass Points of Measures and Orthogonal Polynomials on the Unit Circle

2002 ◽  
Vol 118 (2) ◽  
pp. 257-274
Author(s):  
Leonid Golinskii
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle

Zeros of a family of hypergeometric para-orthogonal polynomials on the unit circle

2013 ◽  
Vol 286 (17-18) ◽  
pp. 1778-1791 ◽  
Author(s):  
Dimitar K. Dimitrov ◽  
A. Sri Ranga
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle

scholarly journals Sobolev Orthogonal Polynomials on the Unit Circle and Coherent Pairs of Measures of the Second Kind

2016 ◽  
Vol 71 (3-4) ◽  
pp. 1127-1149
Author(s):  
F. Marcellán ◽  
A. Sri Ranga
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Sobolev Orthogonal Polynomials ◽  
Coherent Pairs

scholarly journals About several classes of bi-orthogonal polynomials and discrete integrable systems

2014 ◽  
Vol 48 (1) ◽  
pp. 015204 ◽  
Author(s):  
Xiang-Ke Chang ◽  
Xiao-Min Chen ◽  
Xing-Biao Hu ◽  
Hon-Wah Tam
Keyword(s):  
Orthogonal Polynomials ◽  
Integrable Systems ◽  
Discrete Integrable Systems

scholarly journals From orthogonal polynomials on the unit circle to functional equations via generating functions

2015 ◽  
Vol 368 (6) ◽  
pp. 4027-4063 ◽  
Author(s):  
María José Cantero ◽  
Arieh Iserles
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Generating Functions ◽  
Functional Equations

scholarly journals THE GENERALIZED MATRIX VALUED HYPERGEOMETRIC EQUATION

2010 ◽  
Vol 21 (02) ◽  
pp. 145-155 ◽  
Author(s):  
P. ROMÁN ◽  
S. SIMONDI
Keyword(s):  
Differential Equation ◽  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Hypergeometric Functions ◽  
Spherical Functions ◽  
Hypergeometric Equation ◽  
Necessary Condition ◽  
Hypergeometric Differential Equation ◽  
The Matrix ◽  
Generalized Matrix

The matrix valued analog of the Euler's hypergeometric differential equation was introduced by Tirao in [4]. This equation arises in the study of matrix valued spherical functions and in the theory of matrix valued orthogonal polynomials. The goal of this paper is to extend naturally the number of parameters of Tirao's equation in order to get a generalized matrix valued hypergeometric equation. We take advantage of the tools and strategies developed in [4] to identify the corresponding matrix hypergeometric functions nFm. We prove that, if n = m + 1, these functions are analytic for |z| < 1 and we give a necessary condition for the convergence on the unit circle |z| = 1.

Three semi-discrete integrable systems related to orthogonal polynomials and their generalized determinant solutions

Nonlinearity ◽  
2015 ◽  
Vol 28 (7) ◽  
pp. 2279-2306 ◽  
Author(s):  
Xiao-Min Chen ◽  
Xiang-Ke Chang ◽  
Jian-Qing Sun ◽  
Xing-Biao Hu ◽  
Yeong-Nan Yeh
Keyword(s):  
Orthogonal Polynomials ◽  
Integrable Systems ◽  
Discrete Integrable Systems
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