Some Expansion Formulas for Brenke Polynomial Sets

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.