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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 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

On &lt;i&gt;p&lt;/i&gt; and &lt;i&gt;q&lt;/i&gt;-Horn’s Matrix Function of Two Complex Variables

On <i>p</i> and <i>q</i>-Horn’s Matrix Function of Two Complex Variables