Author(s)

Ayman Shehata

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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 ^pH^q 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.

Hypergeometric Matrix functions, p and q-Horn’s Matrix Function, Contiguous Relations, Matrix Functions, Matrix Differential Equation, Differential Operator

A. Shehata, "On p and q-Horn’s Matrix Function of Two Complex Variables," Applied Mathematics, Vol. 2 No. 12, 2011, pp. 1437-1442. doi: 10.4236/am.2011.212203.