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

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Bhatter Sanjay; Nishant -; Purohit Sunil Dutt

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Journal Paper

Paper Information

Journal: SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS (SCMA) Year:2024 | Volume:21 | Issue:2 Page(s): 1-23

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Information Journal Paper

Title

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

Author(s)

Bhatter Sanjay | Nishant - | Purohit Sunil Dutt | Issue Writer Certificate

Keywords

Incomplete gamma function

Incomplete $I$-functions

Mellin-Barnes type contour

Abstract

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.

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