# Complementary Incomplete Gamma Function (G Dataflow)

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Computes the regularized complementary incomplete gamma function.

## x

The input argument.

Default: 0

## a

The lower limit of the regularized complementary incomplete gamma integral.

Default: Positive infinity

## error in

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

Default: No error

## 1 - g(x, a)

Value of the regularized complementary incomplete gamma function.

## error out

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

## Algorithm for Computing the Regularized Complementary Incomplete Gamma Function

The following equation defines the complement of the regularized incomplete gamma function.

${\mathrm{\Gamma }}_{c}\left(x,a\right)=\frac{1}{\mathrm{\Gamma }\left(x\right)}{\int }_{a}^{\infty }{t}^{x-1}{e}^{-t}dt$

The complement of the regularized incomplete gamma function is related to the regularized incomplete gamma function by the following identity.

$\mathrm{\Gamma }\left(x,a\right)+{\mathrm{\Gamma }}_{c}\left(x,a\right)=1$

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

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

For any positive real value of lower limit a, the regularized incomplete gamma function is defined for nonnegative real values of x.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported