The function Γ(n), known as the Gamma function, is a mathematical function that extends the concept of factorials to non-integer values. For positive integers, Γ(n) is defined as (n-1)!, meaning that Γ(5) equals 4! or 24. It is useful in various fields, including statistics and complex analysis, where factorials of non-integer numbers are needed. The Gamma function is defined for all complex numbers except for non-positive integers. It can be expressed using an integral: Γ(z) = ∫₀^∞ t^(z-1)e^(-t) dt for complex number z with a positive real part. This property makes it a powerful tool in advanced mathematics, particularly in probability theory and combinatorics.