**L. P. Castro and M. M. Rodrigues**

##
The Weierstrass-Whittaker Integral Transform

**abstract:**

We introduce a Weierstrass type transform associated with the Whittaker integral
transform, which we refer to as *Weierstrass-Whittaker integral transform*.
We examine some properties of the transform and show, in particular, that it is
helpful in solving of a generalized non-stationary heat equation with an initial
condition.

**Mathematics Subject Classification:** 44A15, 33C15, 33C20,
33C90, 35A22, 35C15, 35K15

**Key words and phrases:** Weierstrass-Whittaker integral transform,
Weierstrass transform, Whittaker integral transform, heat kernel, non-stationary
heat type equation