Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 87, pp. 1-64.

Title: The generalized Airy diffusion equation

Authors: Frank M. Cholewinski (Clemson University, SC, USA)
 James A. Reneke (Clemson University, SC, USA)

Abstract: 
 Solutions of a generalized Airy diffusion equation and an
 associated nonlinear partial differential equation are obtained.
 Trigonometric type functions are derived for a third order
 generalized radial Euler type operator. An associated complex
 variable theory and generalized Cauchy-Euler equations are
 obtained. Further, it is shown that the Airy expansions can be
 mapped onto the Bessel Calculus of Bochner, Cholewinski and
 Haimo.
 
Submitted February 3, 2003. Published August 22, 2003.
Math Subject Classifications: 33C10, 35C05, 44A15.
Key Words: Diffusion polynomial solutions; Bessel calculus; 
           positive definite kernels.