  In this paper, we establish an integral expression for the Dunkl kernel in
the context of Dihedral group of an arbitrary order by using the results in
\cite{M-Y-Vk} where a construction of the Dunkl intertwining operator for a
large set of regular parameter functions is provided. We introduce a
differential equations systems that leads to the explicit expression of the
Dunkl Kernel whenever an appropriate solution of it is obtained. In particular,
an explicit expression of the Dunkl kernel $E_k(x,y)$ is given when one of its
argument $x$ or $y$ is invariant under the action of a known reflection in the
dihedral group. We obtain also a generating series for the homogeneous
components $E_m(x,y)$, $m\in\mathbb{Z}^{+}$, of the Dunkl kernel from which we
derive new sharp estimates for the Dunkl kernel when the parameter function $k$
satisfies $\mathrm{Re}(k)>-\nu$, $\nu$ an arbitrary nonnegative integer, which,
up to our knowledge, is the largest context for such estimates so far.
