# 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.

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.