The Beta Function is a special mathematical function denoted as B(x, y) , defined for positive real numbers x and y . It is expressed in terms of the Gamma Function as B(x, y) = \frac\Gamma(x) \Gamma(y)\Gamma(x+y) . The Beta Function is commonly used in calculus, particularly in the evaluation of integrals and in probability theory. This function has important applications in various fields, including statistics and combinatorics. It can also be interpreted as the area under the curve of the Beta Distribution, which is useful for modeling random variables that are constrained to a finite interval, typically between 0 and 1.