# GAMMAQ

## Purpose:

Computes the regularized complementary incomplete gamma function.

## Syntax:

GAMMAQ(a, x)

 a - A scalar or series, the exponential factor. x - A scalar or series, the integration limit.

## Returns:

A scalar, series, or table.

gammaq(1, 0.5)

returns 0.606531

## Example:

gammaq(1+i, 0.5)

returns 0.855350 + 0.486356i

## Example:

gammaq(1, 0.5i)

returns 0.877583 - 0.479426i

## Example:

gammaq(1..4, 0..3)

returns the series {1, 0.735759, 0.676676, 0.647232}

and is equivalent to:

{gammaq(1,0), gammaq(2,1), gammaq(3,2), gammaq(4,3)}

## Remarks:

The complementary or upper incomplete gamma function is defined as:

GAMMAQ computes the regularized complementary incomplete gamma function defined as:

where P(a, x) is the regularized incomplete gamma function implemented by GAMMAP and Γ(a) is the gamma function implemented by GAMMA .

Since the ordinary gamma function is defined as:

GAMMAQ can be thought of as generalizing the ordinary gamma function with a variable starting integration value.

The limiting values are :

GAMMAQ is also referred to as the regularized upper incomplete gamma function.

See GAMMAINC for an alternate implementation of the incomplete gamma function.