Some Expansion Formulas for Brenke Polynomial Sets
H. Chaggara, A. Gahami and, N. Ben Romdhane

TL;DR
This paper derives explicit expansion formulas for Brenke polynomial sets using generating functions, providing new coefficients expressions and applying results to generalized polynomials, including classical duplication and convolution formulas.
Contribution
It introduces novel explicit expansion formulas for Brenke polynomials and their applications to generalized polynomial families, enhancing computational and theoretical understanding.
Findings
Explicit formulas expressed as finite sums or hypergeometric terms
Applications to generalized Gould-Hopper and Hermite polynomials
Derivation of classical duplication and convolution formulas
Abstract
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.
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Taxonomy
TopicsMathematical functions and polynomials · Advanced Mathematical Identities · Advanced Combinatorial Mathematics
