  By means of the spherical functions associated to the Gelfand pair
$(\mathbb{H}_{n},U(n))$ we define the operator $L+\alpha |T|$, where $L$
denotes the Heisenberg sublaplacian and $T$ denotes de central element of the
Heisenberg Lie algebra, we establish a notion of fundamental solution and
explicitly compute in terms of the Gauss hypergeometric function. For
$\alpha<n$ we use the Integral Representation Theorem to obtain a more detailed
expression. Finally, we remark that when $\alpha=0$ we recover the fundamental
solution for the Heisenberg sublaplacian given by Folland.
