  In this paper, we derive some explicit expansion formulas associated to
Brenke polynomials using operational rules based on their corresponding
generating functions. The obtained coefficients are expressed either in terms
of finite double sums or finite sums or sometimes in closed hypergeometric
terms. The derived results are applied to Generalized Gould-Hopper polynomials
and Generalized Hermite polynomials introduced by Szeg\"{o} and Chihara. Some
well-known duplication and convolution formulas are deduced as particular
cases.
