# GAMMAP

## Purpose:

Computes the regularized incomplete gamma
function.

## Syntax:

GAMMAP(a, x)

a |
- |
A scalar or series, the exponential factor. |

x |
- |
A scalar or series, the integration limit. |

## Returns:

A scalar, series, or table.

## Example:

gammap(1, 0.5)

returns 0.393469

## Example:

gammap(1+i, 0.5)

returns 0.144650
- 0.486356i

## Example:

gammap(1, 0.5i)

returns 0.122417
+ 0.479426i

## Example:

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

returns the series {0,
0.264241, 0.323324, 0.352768}

and is equivalent to:

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

## Remarks:

The incomplete gamma function is defined
as:

GAMMAP computes the regularized incomplete
gamma function defined as:

where Q(a,
x) is the regularized
complementary incomplete gamma function implemented by GAMMAQ
and Γ(*a*)
is the gamma function implemented by GAMMA .

The limiting values are :

Since the ordinary gamma function is defined
as:

GAMMAP can be thought of as generalizing
the ordinary gamma function with a variable integration limit.

GAMMAP is also referred to as the regularized
lower incomplete gamma function.

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

## See Also:

GAMMA

GAMMAINC

GAMMAQ