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On Horn Matrix Function <i>H<sub>2</sub>(A,A′,B,B′;C;z,w)</i> of Two Complex Variables under Differential Operator
Department of Mathematics, Faculty of Science (Suez), Suez Canal University, Suez, Egypt
Department of Mathematics, Faculty of Science (New Valley), Assiut University, New Valley, Egypt
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
Department of Mathematics, College of Science and Arts, Unaizah, Qassim University, Qassim, KSA
- 1 Department of Mathematics, Faculty of Science (Suez), Suez Canal University, Suez, Egypt
- 2 Department of Mathematics, Faculty of Science (New Valley), Assiut University, New Valley, Egypt
- 3 Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
- 4 Department of Mathematics, College of Science and Arts, Unaizah, Qassim University, Qassim, KSA
Advances in Linear Algebra & Matrix Theory·Volume 08 (2018)·Pages 96–110·Published 8 June 2018·DOI10.4236/alamt.2018.82009
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Abstract
The aim of this paper deals with the study of the Horn matrix function of two complex variables. The convergent properties, an integral representation of H 2 (A,A′,B,B′;C;z,w) is obtained and recurrence matrix relations are given. Some result when operating on Horn matrix function with the differential operator D and a solution of certain partial differential equations are established. The Hadamard product of two Horn’s matrix functions is studied, certain results as, the domain of regularity, contiguous functional relations and operating with the differential operator D and D 2 are established.
KeywordsHypergeometric Matrix FunctionHorn Matrix FunctionIntegral FormRecurrence Matrix RelationMatrix Differential EquationDifferential OperatorHadamard Product
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