Hypergeometric Equation in Modeling Relativistic Isotropic Sphere

2013 ◽  
Vol 53 (4) ◽  
pp. 1188-1200 ◽  
Author(s):  
S. Thirukkanesh ◽  
F. C. Ragel
Keyword(s):  
Hypergeometric Equation ◽  
Isotropic Sphere

Optical properties of molecules forming a uniform, uniaxial layer on a small, isotropic sphere

1989 ◽  
Vol 90 (1) ◽  
pp. 556-569 ◽  
Author(s):  
Suzanne Mamiche‐Afara ◽  
Louis Robichaud ◽  
Michael J. Dignam
Keyword(s):  
Optical Properties ◽  
Isotropic Sphere

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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