Gauss Function (G Dataflow)

Version:
Last Modified: January 9, 2017

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