On generalized heat polynomials

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.

Keywords

• generalized heat equation
• source solution
• heat transform
• heat polynomial
• Appell transform
• generating function
• Laguerre polynomial
• hypergeometric function.