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
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])