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])