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

作　　者：Mohamed Saleh Metwally Mahmoud Tawfik Mohamed Ayman Shehata 

机构地区：[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

出　　处：《Advances in Linear Algebra & Matrix Theory》2018年第2期96-110,共15页线性代数与矩阵理论研究进展（英文）

摘　　要：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.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.

关 键 词：HYPERGEOMETRIC MATRIX FUNCTION HORN MATRIX FUNCTION Integral Form Recurrence MATRIX Relation MATRIX DIFFERENTIAL Equation DIFFERENTIAL Operator Hadamard Product 

分 类 号：O1[理学—数学]