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In this study, the complex interactions between the well-known Mittag-Leffler functions with two, three, and four parameters are explored. We first study the integral forms of the Mittag-Leffler function E, ^, (z) with the goal of clarifying its mathematical behaviours and features. Moreover, we create relations between these functions and generalised hypergeometric functions and Fox-Wright functions, expanding the range of their use and comprehension. We explore a number of unique situations by in-depth examination, providing insight into the subtle characteristics of these functions. This investigation advances our theoretical knowledge and opens up possibilities for future applications in a number of scientific fields. As such, this study adds to the current conversation in mathematical analysis and is an important tool for both practitioners and researchers.
Pooja Singh (Wed,) studied this question.