Complementary error function: erfc

### 4.9.6 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
| )

Check :
normal_cdf(1)=0.841344746069