Certain expansion formulae involving the Y-function and its associated functions

Abstract

 In mathematical analysis, special functions are essential, especially when it comes to obtaining representations that highlight their structural and analytic characteristics. In this paper we concentrate on the Y-function, a generalized version of hypergeometric-type functions and their extensions presented by Yang. The generalized Taylor’s series formula, which extends the traditional Taylor series to fractional orders, is used in the work to create some expansion formulae involving the Y-function and its related families. This method highlights the analytic richness and structural flexibility of the Y-function framework by deriving novel series representations. These findings advance the theoretical understanding of generalized special functions in the framework of fractional calculus and generalize already existing expansion connections.