GAMMAQ

Purpose:

Computes the regularized complementary incomplete gamma function.

GAMMAQ(a, x)

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

A scalar, series, or table.

gammaq(1, 0.5)

returns 0.606531

gammaq(1+i, 0.5)

returns 0.855350 + 0.486356i

gammaq(1, 0.5i)

returns 0.877583 - 0.479426i

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)}

The complementary or upper incomplete gamma function is defined as:

$image\gammq01.gif$

GAMMAQ computes the regularized complementary incomplete gamma function defined as:

$image\gammq02.gif$

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:

$image\gamma03.gif$

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

The limiting values are :

$image\gammq03.gif$

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

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