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On Horn Matrix Function H2(A,A′,B,B′;C;z,w) of Two Complex Variables under Differential Operator

DOI: 10.4236/alamt.2018.82009, PP. 96-110

Keywords: Hypergeometric Matrix Function, Horn Matrix Function, Integral Form, Recurrence Matrix Relation, Matrix Differential Equation, Differential Operator, Hadamard Product

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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 H2(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 D2 are established.

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