Complementary error function: erfc

### 2.9.6 Complementary error function: `erfc`

`erfc` takes as argument a number a.
`erfc` returns the value of the complementary error function at x=a, this function is defined by :

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

Hence erfc(0)=1, since :

∫ |
+∞
0
| e−t2dt= |
√ |
π
2

Input :

`erfc(1)`

Output :

`0.15729920705`

Input :

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

Output :

`0.841344746069`

Remark
The relation between `erfc` and `normal_cdf` is :

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

Verification :
`normal_cdf(1)=0.841344746069`