![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Beta_function.svg/640px-Beta_function.svg.png&w=640&q=50)
Beta function
Mathematical function / From Wikipedia, the free encyclopedia
This article is about the Euler beta function. For other uses, see Beta function (disambiguation).
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
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Beta_function.svg/320px-Beta_function.svg.png)
for complex number inputs
such that
.
The beta function was studied by Leonhard Euler and Adrien-Marie Legendre and was given its name by Jacques Binet; its symbol Β is a Greek capital beta.