We introduce multivariable generalized forms of Hermite polynomials and analyze both the Gould-Hopper type polynomials and more general forms, which are analogues of the classical orthogonal polynomials, since they represent a basis in L2(RN) Hilbert space, suitable for series expansion of square summable functions of N variables: Moreover, the role played by these generalized Hermite polynomials in the solution of evolution-type differential equations is investigated: The key-note of the method leading to the multivariable polynomials is the introduction of particular generating functions, following the same criteria underlying the theory of multivariable generalized Bessel functions. © 1994.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Computational Mathematics
- Modelling and Simulation