Communications of the
Korean Mathematical Society CKMS

In this paper, we discuss how the operational calculus can be exploited to the theory of generalized special functions of many variables and many indices. We obtained the generating relations for 3-index, 3-variable and 1-parameter Hermite polynomials. Some mixed type generating relations and bilateral generating relations of many indices and many variable like Lagurre-Hermite and Hermite-Sister Celine's polynomials are also obtained. Further we generalize some results on old symbolic notations using operational identities.

Keywords: operational calculus, special functions, mixed generating functions, bilateral generating relations

MSC numbers: 33C45, 33C47, 33C65, 33B10