# The lower incomplete γ function: igamma

### 5.8.15 The lower incomplete γ function: igamma

The lower incomplete γ function is defined by

γ(a,b) =

∫

b
0

e−tta−1 dt.

The igamma command computes the lower incomplete γ function.

- igamma takes two mandatory arguments and one optional argument:
  - a, a number.
  - b, a positive real number.
  - Optionally, the number 1.
- igamma(a,b) returns γ(a,b).
- igamma(a,b,1) returns a normalized version of the function; namely γ(a,b)/Γ(a).

#### Examples.

- Input:
  igamma(4.0,3.0)
  Output:

  2.11660866731

- Input:
  igamma(4.0,3.0,1)
  Output:

  0.352768111218

  since Γ(4) = 6 and 2.11660866731/6 = 0.352768111218.