# gleam_community/maths/special

Special: A module containing special mathematical functions.

**Special mathematical functions**

# Functions

`pub fn beta(x: Float, y: Float) -> Float`

The beta function over the real numbers:

\[ \text{B}(x, y) = \frac{\Gamma(x) \cdot \Gamma(y)}{\Gamma(x + y)} \]

The beta function is evaluated through the use of the gamma function.

`pub fn gamma(x: Float) -> Float`

The gamma function over the real numbers. The function is essentially equal to the factorial for any positive integer argument: $$\Gamma(n) = (n - 1)!$$

The implemented gamma function is approximated through Lanczos approximation using the same coefficients used by the GNU Scientific Library.

```
pub fn incomplete_gamma(a: Float, x: Float) -> Result(
Float,
String,
)
```

The lower incomplete gamma function over the real numbers.

The implemented incomplete gamma function is evaluated through a power series expansion.