The Gamma function is a mathematical function that extends the concept of factorials to non-integer values. For positive integers, the Gamma function is defined as Γ(n) = (n-1)!, meaning that it produces the same result as the factorial of one less than the integer. It is defined for all complex numbers except for negative integers. The Gamma function is often used in various fields such as statistics, probability theory, and complex analysis. It plays a crucial role in defining distributions like the Gamma distribution and the Beta distribution, making it a valuable tool in both theoretical and applied mathematics.