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

Examples

>>> igam(1, 2)
0.8646647167633873
>>> igam([1,1], [2,3])
array([ 0.86466472,  0.95021293])