The Gamma Function, denoted by Γ(z), is a mathematical function that extends the concept of factorial to complex and real numbers. It is defined as the integral of t^(z-1)e^(-t) from 0 to infinity.
Some of the properties of the Gamma Function include:
The Gamma Function is an extension of the Factorial Function to complex and real numbers. For positive integers n, Γ(n+1) = n!, which means that the Gamma Function can be used to calculate factorials for non-integer values as well.
The Gamma Function has many applications in mathematics, physics, and engineering. Some common applications include:
The Gamma Function and the Beta Function are closely related. In fact, the Beta Function can be expressed in terms of the Gamma Function as B(x,y) = Γ(x)Γ(y)/Γ(x+y). This relationship is useful in calculating integrals and solving problems in probability and statistics.