igam¶

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

Calculate the regularized incomplete Gamma function (lower).

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

Parameters:	a (scalar or array) – a > 0 x (scalar or array) – x > 0
Returns:	val – The incomplete Gamma function of the input.
Return type:	scalar or array

See also

gamma(), igamc()

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

[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

>>> igam(1, 2)
0.8646647167633873

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