Complementary error function: erfc

### 6.8.12 Complementary error function: erfc

The complementary error function is defined by

erfc(x)= |
2
√ |
π
| ∫ |
+∞
x
| e−t2dt=1−erf(x)

Hence erfc(0)=1, since

∫ |
+∞
0
| e−t2dt= |
√ |
π
2

The erfc command computes the complementary error function.

- erfc takes one argument:
  a, a number.
- erfc(a) returns the value of the complementary error function erfc(a).

Examples.

- Input:
  erfc(1)
  Output:

  1−erf | ⎛ ⎝ | 1 | ⎞ ⎠

- Input:
  1- erfc(1/(sqrt(2)))*0.5
  Output:

  0.841344746069

Remark.
The relation between erfc and normal_cdf (see Section 9.4.7) is:

normal_cdf(x) =1− |
1
2
| erfc ( |
x
√ |
2
| )

Check:
Input:

normal_cdf(1.0)

Output:

0.841344746069