# Complementary error function: erfc

### 5.8.12 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 8.4.7) is:

normal_cdf(x) =1−

1
2

erfc (

x

√

2

)

Check:
Input:

normal_cdf(1.0)

Output:

0.841344746069