Difference between revisions of "Manuals/calci/ERF"

Revision as of 23:06, 25 December 2013

ERF(ll,ul)

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: $ERF(z)={\frac {2}{\sqrt {\pi }}}\int \limits _{0}^{z}e^{-t^{2}}dt$

$ERF(a,b)={\frac {2}{\sqrt {\pi }}}\int \limits _{a}^{b}e^{-t^{2}}dt=ERF(b)-ERF(a)$ .

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 *Also <math>ul</math> is optional. When we are omitting the <math>ul</math> value, then the  integral of the error function between 0 and the given <math>ll</math> value is returned otherwise it will consider the given <math>ll</math> and <math>ul</math> values.
 *This function is also called Gauss error function.<math>ERF </math>is defined by:                                        <math>ERF(z)=\frac {2}{\sqrt{\pi}}\int\limits_{0}^{z}e^{-t^2} dt</math>
-<math>ERF(a,b)=\frac{2}{\sqrt{\pi}\int\limits_{a}^{b}e^{-t^2} dt=ERF(b)-ERF(a)</math>.
+<math>ERF(a,b)=\frac{2}{\sqrt{\pi}}\int\limits_{a}^{b}e^{-t^2} dt=ERF(b)-ERF(a)</math>.
 *In this case 'a' is the lower limit and 'b' is the upper limit.
 *This function will return the result as error when