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:

 

image\gammp01.gif

 

GAMMAP computes the regularized incomplete gamma function defined as:

 

image\gammp02.gif

 

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 :

 

image\gammp03.gif

 

Since the ordinary gamma function is defined as:

 

image\gamma03.gif

 

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