Computes the regularized incomplete gamma function.
GAMMAP(a, x)
a |
- |
A scalar or series, the exponential factor. |
x |
- |
A scalar or series, the integration limit. |
A scalar, series, or table.
gammap(1, 0.5)
returns 0.393469
gammap(1+i, 0.5)
returns 0.144650 - 0.486356i
gammap(1, 0.5i)
returns 0.122417 + 0.479426i
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)}
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
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.