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On <i>p</i> and <i>q</i>-Horn’s Matrix Function of Two Complex Variables
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Applied Mathematics·Volume 02 (2011)·Pages 1437–1442·Published 5 December 2011·DOI10.4236/am.2011.212203
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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 <sup>p</sup>H<sup>q</sup> <sub>2</sub> is obtained, recurrence relations are established. Finally, we obtain a higher order partial differential equation satisfied by the <i>p</i> and <i>q</i>-Horn’s matrix function.
KeywordsHypergeometric Matrix functionsp and q-Horn’s Matrix FunctionContiguous RelationsMatrix FunctionsMatrix Differential EquationDifferential Operator
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