# Stirling's Formula (G Dataflow)

Computes the Stirling approximation to the gamma function.

## x

Input argument. If x is negative, the node uses the absolute value of x.

Default: 0

## error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

## Stirling(x)

Value of the Stirling function.

## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## 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

Web Server: Not supported in VIs that run in a web application