International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 2, Pages 393-400
doi:10.1155/S0161171288000456
On generalized heat polynomials
Department of Mathematics and Statistics, The University of Calgary, Calgary T2N 1N4, Alberta, Canada
Received 18 March 1987
Copyright © 1988 C. Nasim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We consider the generalized heat equation of nth order ∂2u∂r2+n−1r∂u∂r−α2r2u=∂u∂t. If the initial temperature is an even power function, then the heat transform with the source solution as the kernel gives the heat polynomial. We discuss various properties of the heat polynomial and its Appell transform. Also, we give series representation of the heat transform when the initial temperature is a power function.