# Stirling's Formula (G Dataflow)

Version:

Computes the Stirling approximation to the gamma function.

## x

The input argument.

Default: 0

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error

## Stirling(x)

Value of the Stirling function.

## error out

Error information. The node produces this output according to standard error behavior.

## Algorithm for Computing the Stirling Approximation to the Gamma Function

The following approximation defines the Stirling approximation to the gamma function.

$\mathrm{\Gamma }\left(x\right)\approx {e}^{-x}{x}^{x-1/2}{\left(2\pi \right)}^{1/2}\left[1+\frac{1}{12x}+\frac{1}{288{x}^{2}}-\frac{139}{51840{x}^{3}}-\frac{571}{2488320{x}^{4}}+...\right]$

The function is defined according to the following interval for the input value.

$x\in \left[0,\infty \right)$

This node supports the entire domain of this function that produces real-valued results. The function is defined for nonnegative real values of x.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported