igamc

sherpa.utils.igamc(a, x)[source] [edit on github]

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

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
Parameters:
ascalar or array

a > 0

xscalar or array

x > 0

Returns:
valscalar or array

The incomplete Gamma function of the input.

See also

gamma, igam

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.

Examples

>>> igamc(1, 2)
0.1353352832366127

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