scholarly journals Integrable Dynamics of Charges Related to the Bilinear Hypergeometric Equation

2003 ◽  
Vol 242 (1-2) ◽  
pp. 251-275 ◽  
Author(s):  
Igor Loutsenko
Keyword(s):  
Hypergeometric Equation ◽  
Integrable Dynamics

scholarly journals Yang–Baxter maps and integrable dynamics

2003 ◽  
Vol 314 (3) ◽  
pp. 214-221 ◽  
Author(s):  
A.P. Veselov
Keyword(s):  
Integrable Dynamics

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.

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