Manuals/calci/ERF

ERF(a,b,accuracy)

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 $ERF(a,b,accuracy)$ , $a$ is the lower limit of the integrating function and $b$ is the upper limit of the integrating function.
Also $b$ is optional. When we are omitting the $b$ value, then the integral of the error function between 0 and the given $a$ value is returned otherwise it will consider the given $a$ and $b$ 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. $a$  or  $b$  is negative.

The syntax is to calculate error function in ZOS is .
- $a$ is the lower limit and $b$ is the upper limit.
- $accuracy$ gives accurate value of the solution.
For e.g.,erf(2,3),erf(2,3,0.001)