Evaluation of improper integrals involving incomplete I-functions and related special forms

Abstract

This paper presents a comprehensive study of improper integrals involving generalized incomplete $I$-functions. By employing the Mellin–Barnes integral framework, we derive a unified class of infinite integral representations encapsulating a wide range of incomplete special functions. Several corollaries are provided as special instances by appropriately selecting the parameters of the incomplete $I$-function, yielding results connected to other well-known incomplete functions such as the incomplete $H$-function and $G$-type functions. The findings extend known results and contribute a versatile tool for further applications in mathematical physics and applied analysis.