Some identities of Fubini numbers related to special numbers

In this paper, we examine the interconnections between Fubini numbers and a range of recently defined special numbers, including the Lah-Bell numbers, the Changhee numbers, and the Dahee numbers, along with several other established special numbers. We explore these relationships by analysing the generating functions associated with these numbers, which enables us to establish diverse formulae for Fubini numbers in relation to other special numbers. Additionally, we uncover new properties of Fubini numbers through this investigation. Furthermore, by employing formal power series of generating functions, we establish general identities for special numbers, thereby extending our understanding of their properties and relationships. Finally, we study the interconnections of the five special functions by observing the shape of functions.