Heat polynomial analogues for equations with higher order time derivatives

We generalize the heat polynomials for the heat equation to more general partial differential equations, of higher order with respect to both the time variable and the space variables. Whereas the heat equation requires only one family of polynomials, for an equation of the th order with respect to time we introduce families of polynomials. These families correspond to the initial conditions specified by the Cauchy problem.  2004 Elsevier Inc. All rights reserved