Leveraging functional equations to determine the Generalized Gamma Function of one and two variables with certain constraints (KEY IJP************923)

• Ananaya Shukal,Chinta Mani Tiwari

Abstract

Functional equations serve as powerful tools in mathematical analysis, providing insights into the behavior and properties of various mathematical functions. In this study, we leverage functional equations to determine the Generalized Gamma Function of one and two variables under specific constraints. The Generalized Gamma Function, denoted as _k (x), is a fundamental mathematical function with wide-ranging applications in probability theory, mathematical physics, and engineering. By formulating and solving functional equations governing the Generalized Gamma Function, we establish connections between its parameters and uncover its underlying structure. Furthermore, we extend our analysis to the two-variable case, exploring functional equations with additional constraints. Through analytical techniques and numerical simulations, we elucidate the behavior of the Generalized Gamma Function under different conditions, providing valuable insights into its properties and applications. This research contributes to a deeper understanding of the Generalized Gamma Function and its utility in mathematical modeling and analysis.