Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 27, No. 1, pp. 41-49 (2011)

Operational rules and arbitrary order two-index two-variable Hermite matrix generating functions

M. S. Metwally

Suez Canal University

Abstract: The main aim of this paper is to introduce generalized forms of operational rules associated with operators corresponding to a generalized Hermite matrix polynomials expansions. The associated generating functions is reformulated within the framework of an operational formalism and the theory of exponential operators. We obtain to unilateral and bilateral generating functions by using the same procedure. Possible extensions of the technique are also discussed.

Keywords: Operators; Transfer operators; Matrix functions; Hermite matrix polynomials; Hermite matrix differential equation; Generating functions

Classification (MSC2000): 33C45; 33E20

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