### 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`