# beta

beta(x, y)

Euler integral of the first kind \$\operatorname{B}(x,y) = \Gamma(x)\Gamma(y)/\Gamma(x+y)\$.

## Examples

In the Julia programming language, the function `beta(x, y)` calculates the Euler integral of the first kind, also known as the beta function. It is defined as:

``julia> beta(x, y)``

The beta function is calculated as `Gamma(x) * Gamma(y) / Gamma(x + y)`, where `Gamma` represents the gamma function.

Here are some examples of how to use the `beta` function:

1. Calculate the beta function for positive integers:

``````julia> beta(3, 4)
0.03333333333333333``````

This example calculates the beta function for `x = 3` and `y = 4`.

2. Calculate the beta function for non-integer values:

``````julia> beta(0.5, 0.5)
3.141592653589793``````

It calculates the beta function for `x = 0.5` and `y = 0.5`.

3. Calculate the beta function with variables:
``````julia> x = 2;
julia> y = 3;
julia> beta(x, y)
0.08333333333333333``````

In this example, the beta function is calculated using variables `x` and `y`.

It is important to note that the `beta` function requires the `Gamma` function, so make sure that the `Gamma` function is available when using the `beta` function.