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The Gamma function is a fundamental concept in mathematics that extends the factorial function to complex numbers. It is defined for positive integers, non-integers and complex values, except for non-positive integers. This function exhibits several important properties. It satisfies the recurrence relation. It is meromorphic, meaning it is analytic except for its simple poles at non-positive integers. It plays a critical role in various branches of mathematics and applied sciences, including probability theory, complex analysis, and mathematical physics. In probability and statistics, it helps in defining distributions such as the Gamma and Beta distributions. In physics, it appears in the solutions of differential equations and in the formulation of certain integral transforms. This book provides significant information on Gamma function in mathematics to help develop a good understanding of the subject. It elucidates the concepts and innovative models around prospective developments with respect to Gamma functions. Those in search of information to further their knowledge will be greatly assisted by this textbook.