Manuals/calci/ERF

ERF(ll,ul)

Description

This function gives the value of the error function .
Error function is the special function which is encountered in integrating the normal distribution.
In $ERF(ll,ul),ll$ is the lower limit of the integrating function and $ul$ is the upper limit of the integrating function.
Also $ul$ is optional. When we are omitting the $ul$ value, then the integral of the error function between 0 and the given $ll$ value is returned otherwise it will consider the given $ll$ and $ul$ values.
This function is also called Gauss error function.
$ERF$ is defined by: $ERF(z)={\frac {2}{\sqrt {\pi }}}\int \limits _{0}^{z}e^{-t^{2}}dt$
$ERF(a,b)={\frac {2}{\sqrt {\pi }}}\int \limits _{a}^{b}e^{-t^{2}}dt=ERF(b)-ERF(a)$ .
In this case $a$ is the lower limit and $b$ is the upper limit.
This function will return the result as error when

1.any one of the argument is non-numeric.
2. $ll$  or  $ul$  is negative.