The Beta function is a special mathematical function that is often used in calculus and statistics. It is defined for two positive numbers, x and y , and is represented as B(x, y) . The function can be expressed in terms of the Gamma function, another important mathematical function, using the formula B(x, y) = \frac\Gamma(x) \Gamma(y)\Gamma(x+y) . The Beta function has applications in various fields, including probability theory and combinatorics. It is particularly useful for calculating probabilities in beta distributions, which are commonly used in statistics to model random variables limited to a finite range.