Manuals/calci/ERF

ERF(a,b,accuracy)

• $a$ is the lower limit and $b$ is the upper limit.
• $accuracy$ gives accurate value of the solution

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.

ZOS Section

• The syntax is to calculate error function in ZOS is $ERF(a,b,accuracy)$.
  • $a$ 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)

Examples

1. ERF(1,2)=0.15262153
2. ERF(3,2)=-0.004655645
3. ERF(0,1)=0.842700735
4. ERF(5)=1
5. ERF(-3)=NAN

See Also

• ERFC

References

Error Function