A new class of Tricomi-Legendre-Hermite and related polynomials

In this paper we introduce a new class of generalized Hermite-Legendre polynomials of 2-variables and consequently a new class of Tricomi, Bessel and Hermite polynomials and their generalizations starting from suitable generating functions. The theory of Bessel, Legendre, Hermite and of the associated generating functions and their generalizations is reformulated within the framework of a series rearrangement formalism by using different analytical means on their respective generating functions.