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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Vydané v:Linear & multilinear algebra Ročník 62; číslo 3; s. 347 - 361
Hlavný autor: Salem, Ahmed
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Abingdon Taylor & Francis 04.03.2014
Taylor & Francis Ltd
Predmet:
15A15
Algebra
basic Gauss hypergeomtric function
Convergence
Mathematical analysis
matrix functional calculus
matrix q-difference equation
Representations
ISSN:0308-1087, 1563-5139
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Abstract 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.
AbstractList 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 [Formula omitted.] -derivative is bounded are determined. Hypergeometric matrix [Formula omitted.] -difference equation is introduced and two solutions to this equation are found as terms of basic Gauss hypergeometric matrix function. The [Formula omitted.] -integral representation for this matrix function is established. [PUBLICATION ABSTRACT]
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.
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 [Image omitted.]-derivative is bounded are determined. Hypergeometric matrix [Image omitted.]-difference equation is introduced and two solutions to this equation are found as terms of basic Gauss hypergeometric matrix function. The [Image omitted.]-integral representation for this matrix function is established.
Author Salem, Ahmed
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  organization: Faculty of Science, Department of Mathematics, Al Jouf University
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SubjectTerms 15A15
Algebra
basic Gauss hypergeomtric function
Convergence
Mathematical analysis
matrix functional calculus
matrix q-difference equation
Representations
Title The basic Gauss hypergeometric matrix function and its matrix q-difference equation
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