Question

convergence of beta function​

Answer 1

Answer:

In mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients. It is defined by the integral for complex number inputs x, y such that Re x > 0, Re y > 0.

The beta function was studied by Euler and Legendre and was given its name by Jacques Binet; its symbol Β is a Greek capital beta.

The beta function is symmetric, meaning that for all inputs x and y, A key property of the beta function is its close relationship to the gamma function.

The beta function is also closely related to binomial coefficients. When x and y are positive integers, it follows from the definition of the gamma function.