igamc

Synopsis

Calculate the complement of the regularized incomplete Gamma function (upper).

Syntax

igamc(a, x)

a - scalar or array
x - scalar or array

Description

The function is defined using the regularized incomplete Gamma function - igam(a,x) - and the Gamma function - gamma(a) - as:

igamc(a,x) = 1 - igam(a,x)
           = 1 / gamma(a) Int_x^Inf e^(-t) t^(a-1) dt

Examples

Example 1

>>> igamc(1, 2)
0.1353352832366127

Example 2

>>> igamc([1,1], [2,3])
array([ 0.13533528,  0.04978707])

PARAMETERS

The parameters for this function are:

Parameter	Definition
a	a > 0
x	x > 0

Return value

The return value from this function is:

val -- The incomplete Gamma function of the input.

Notes

In this implementation, which is provided by the Cephes Math Library [1] , both arguments must be positive. The integral is evaluated by either a power series or continued fraction expansion, depending on the relative values of a and x. Using IEEE arithmetic, the relative errors are

domain	domain	# trials	peak	rms
0.5,100	0,100	200000	1.9e-14	1.7e-15
0.01,0.5	0,100	200000	1.4e-13	1.6e-15

References

[1] Cephes Math Library Release 2.0: April, 1987. Copyright 1985, 1987 by Stephen L. Moshier. Direct inquiries to 30 Frost Street, Cambridge, MA 02140.

Bugs

See the bugs pages on the Sherpa website for an up-to-date listing of known bugs.