Author(s)

Mohamed Saleh Metwally¹, Mahmoud Tawfik Mohamed², Ayman Shehata^3,4*

¹Department of Mathematics, Faculty of Science (Suez), Suez Canal University, Suez, Egypt.
²Department of Mathematics, Faculty of Science (New Valley), Assiut University, New Valley, Egypt.
³Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt.
⁴Department of Mathematics, College of Science and Arts, Unaizah, Qassim University, Qassim, KSA.

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.

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

Metwally, M. , Mohamed, M. and Shehata, A. (2018) On Horn Matrix Function H₂(A,A′,B,B′;C;z,w) of Two Complex Variables under Differential Operator. Advances in Linear Algebra & Matrix Theory, 8, 96-110. doi: 10.4236/alamt.2018.82009.