Some properties of Legendre–Gould Hopper polynomials and operational methods

In this paper, the author introduces the Legendre–Gould Hopper polynomials by combining the operational methods with the principle of monomiality. Generating functions, series definition, differential equation and certain other properties of Legendre–Gould Hopper polynomials are derived. Further, operational representations of these polynomials are established, which are used to get integral representations and expansion formulae. Certain summation formulae for these polynomials are also obtained.