Some New Results for the \mathscr{M}-Transform Involving the Incomplete I-Functions

Integral transformations are crucial for solving a variety of actual issues. The right choice of integral transforms aids in simplifying both integral and differential problems into a solution-friendly algebraic equation. In this paper, \mathscr{M}-transform is applied to establish the image formula for the multiplication of a family of polynomials and incomplete I-functions. Additionally, we discovered image formulations for a few significant and valuable cases of incomplete I-functions. Numerous previously unknown and novel conclusions can be reached by assigning specific values to the parameters involved in the primary conclusions drawn in this study.

کلیدواژه ها:

Incomplete gamma function ، Incomplete I-functions ، Mellin-Barnes type contour