Kucukoglu, Irem2026-01-242026-01-242023https://hdl.handle.net/20.500.12868/4746In this paper, it is aimed to introduce a unification and generalization of the generating functions for Sheffer type sequences such as the Peters polynomials, the Boole polynomials, the Changhee polynomials, the Korobov polynomials of the first kind and the Peters-type Simsek numbers and polynomials. Moreover, by considering a special case of the aforementioned unification, we also introduce and investigate a new family of numbers and polynomials to be referred as the more general kind of the Peters-type Simsek numbers and polynomials. Finally, we give some applications of our findings. © 2023, MTJPAM Turkey. All rights reserved.eninfo:eu-repo/semantics/closedAccesscomputation formulasFibonacci type numbers and polynomialsGenerating functionsPeters-type Simsek numbers and polynomialsrecurrence relationsSheffer sequencesspecial functionsspecial numbers and polynomialsArticle5271882-s2.0-85181923321Q1