# Gauss Function (G Dataflow)

Version:

Computes the Gauss hypergeometric function according to a specific input argument and parameters.

## x

The input argument.

Default: 0

## a

The first parameter of the Gauss hypergeometric function.

## b

The second parameter of the Gauss hypergeometric function.

## c

The third parameter of the Gauss hypergeometric function.

## error in

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

Default: No error

## F(x, a, b, c)

Value of the Gauss hypergeometric function.

## error out

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

## Algorithm for Computing the Gauss Function

The Gauss hypergeometric function F(x, a, b, c) is a solution of the following differential equation:

$x\left(1-x\right)\frac{{d}^{2}w}{d{x}^{2}}+\left[c-\left(a+b+1\right)x\right]\frac{dw}{dx}-abw=0$

The function is defined according to the following intervals for the input values.

$a,b,c\in \Re ,x\in \left(-\infty ,1\right)$
$\left(c>a+b\right)⇒x\in \left(-\infty ,1\right]$

This node supports the entire domain of this function that produces real-valued results. For any real value of a, b, and c, the function is defined for real values of x < 1. For real values of a, b, and c, such that c > a + b, the domain of x is extended to include 1.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported