The basic Gauss hypergeometric matrix function and its matrix q-difference equation

In this paper, the basic Gauss hypergeometric matrix function is introduced and studied. The ratio test is used to determine the radius of convergence in which this matrix function is absolutely convergent. The domains in which the basic Gauss hypergeometric matrix function is invertible and its -de...

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Bibliographic Details
Published in:Linear & multilinear algebra Vol. 62; no. 3; pp. 347 - 361
Main Author: Salem, Ahmed
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 04.03.2014
Taylor & Francis Ltd
Subjects:
15A15
Algebra
basic Gauss hypergeomtric function
Convergence
Mathematical analysis
matrix functional calculus
matrix q-difference equation
Representations
ISSN:0308-1087, 1563-5139
Online Access:Get full text
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Summary:In this paper, the basic Gauss hypergeometric matrix function is introduced and studied. The ratio test is used to determine the radius of convergence in which this matrix function is absolutely convergent. The domains in which the basic Gauss hypergeometric matrix function is invertible and its -derivative is bounded are determined. Hypergeometric matrix -difference equation is introduced and two solutions to this equation are found as terms of basic Gauss hypergeometric matrix function. The -integral representation for this matrix function is established.
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ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2013.777437