  In the first part of this paper, we express the generalized Bessel function
associated with dihedral systems and a constant multiplicity function as a
infinite series of confluent Horn functions. The key ingredient leading to this
expression is an extension of an identity involving Gegenbauer polynomials
proved in a previous paper by the authors, together with the use of the Poisson
kernel for these polynomials. In particular, we derive an integral
representation of this generalized Bessel function over the standard simplex.
The second part of this paper is concerned with even dihedral systems and
boundary values of one of the variables. Still assuming that the multiplicity
function is constant, we obtain a Laplace-type integral representation of the
corresponding generalized Bessel function, which extends to all even dihedral
systems a special instance of the Laplace-type integral representation proved
in \cite{Amr-Dem}.
