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) = $${\frac{{2}}{{\sqrt{\pi}}}}$$$$\int_{x}^{{+\infty}}$$e^-t2dt = 1 - erf (x)

Hence erfc(0) = 1, since :

$$\int_{0}^{{+\infty}}$$e^-t2dt = $${\frac{{\sqrt{\pi}}}{{2}}}$$

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 :

$$\mbox{\tt normal\_cdf}(x)=1-\frac{1}{2}\*\mbox{\tt erfc} (\frac{x}{\sqrt{2}})$$

Verification :
normal_cdf(1)=0.841344746069