TITLE:
On p and q-Horn’s Matrix Function of Two Complex Variables
AUTHORS:
Ayman Shehata
KEYWORDS:
Hypergeometric Matrix functions, p and q-Horn’s Matrix Function, Contiguous Relations, Matrix Functions, Matrix Differential Equation, Differential Operator
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.12,
December
5,
2011
ABSTRACT: The main aim of this paper is to define and study of a new Horn’s matrix function, say, the p and q-Horn’s matrix function of two complex variables. The radius of regularity on this function is given when the positive integers p and q are greater than one, an integral representation of pHq 2 is obtained, recurrence relations are established. Finally, we obtain a higher order partial differential equation satisfied by the p and q-Horn’s matrix function.