Certain Expansion Formulae for Incomplete W-Function and Other Related Special Functions

Abstract

This research work establishes expansion formulae for the generalised incomplete W-functions

and several of their important reductions, including the incomplete Y-functions and incomplete I-functions.

Using Osler’s generalised Taylor expansion together with fractional derivatives, series representations that

express each function in terms of higher-order W-type functions with shifted parameter sets are derived. The

identities presented here extend these results and provide a unified expansion framework for the broader W-

family. The formulae obtained through this study can find their applications in fractional calculus, integral

equations, and other areas involving Mellin–Barnes kernel