igamc

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

Calculate the complement of the regularized incomplete Gamma function (upper).

The function is defined using the regularized incomplete Gamma function - igam(a,x) - and the Gamma function - gamma(a) - as:

```igamc(a,x) = 1 - igam(a,x)
= 1 / gamma(a) Int_x^Inf 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

domain

# trials

peak

rms

0.5,100

0,100

200000

1.9e-14

1.7e-15

0.01,0.5

0,100

200000

1.4e-13

1.6e-15

References

Examples

```>>> igamc(1, 2)
0.1353352832366127
```
```>>> igamc([1,1], [2,3])
array([ 0.13533528,  0.04978707])
```