igam

Synopsis

Calculate the regularized incomplete Gamma function (lower).

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:

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

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.

See Also

tools::response

color_color, modelflux

tools::statistics

aprates

utilities

calc_chisqr, calc_energy_flux, calc_model_sum, calc_photon_flux, calc_source_sum, calc_stat, gamma, igamc, incbet, lgam