Last modified: December 2020

URL: https://cxc.cfa.harvard.edu/sherpa/ahelp/igam.html
AHELP for CIAO 4.13 Sherpa v1

igam

Context: utilities

Synopsis

Calculate the regularized incomplete Gamma function (lower).

Syntax

igam(a, x)

a - scalar or array
x - scalar or array

Description

The function is defined using the complete Gamma function - gamma(a) - as:

igam(a,x) = 1 / gamma(a) Int_0^x e^(-t) t^(a^-1) dt

Examples

Example 1

>>> igam(1, 2)
0.8646647167633873

Example 2

>>> igam([1,1], [2,3])
array([ 0.86466472,  0.95021293])

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 # trials peak rms
0,30 200000 3.6e-14 2.9e-15
0,100 300000 9.9e-14 1.5e-14

References


Bugs

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

See Also

tools
aprates, modelflux
utilities
calc_chisqr, calc_energy_flux, calc_model_sum, calc_photon_flux, calc_source_sum, calc_stat, gamma, igamc, incbet, lgam