### 7.3.12 Complementary error function

The complementary error function is defined by

erfc(x)=

2

√

π

∫

+∞
x

e−t2d t=1−erf(x).

Hence erfc(0)=1, since

∫

+∞
0

e−t2d t=

√

π

2

.

The erfc command computes the complementary error function.

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

#### Examples

erfc(1)

1−erf | ⎛ ⎝ | 1 | ⎞ ⎠

1-erfc(1/(sqrt(2)))*0.5

0.841344746069 |  |  |  |  |  |  |  |  |  |

##### Remark.

The relation between erfc and normal_cdf (see Section 20.4.7) is:

normal_cdf(x) =1−

1
2

erfc

⎛
⎜
⎜
⎜
⎜
⎝

x

√

2

⎞
⎟
⎟
⎟
⎟
⎠

.