Abstract

In this paper, we study differential equations arising from the generating functions of the 3-variable Hermite polynomials. We give explicit identities for the 3-variable Hermite polynomials. Finally, we investigate the zeros of the 3-variable Hermite polynomials by using computer.

Keywords: differential equations, heat equation, Hermite polynomials, the 3-variable Hermite polynomials, generating functions, complex zeros
