In this paper, new and general classes of multi-variable Hermite-Tricomi functions are introduced and some properties of these functions are established. Further, generating relations for Laguerre-Hermite polynomials involving various forms of Hermite-Tricomi functions are derived.
Recently, many extensions of some special functions are defined by using the extended Beta function. In this paper, we introduce a new generalization of extended Gegenbauer polynomials of two variables by using the extended Gamma function. Some properties of these generalized polynomials such as integral representation, recurrence relation and generating functions are obtained.
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