Re: Integrating Gaussians
- To: mathgroup at yoda.ncsa.uiuc.edu
- Subject: Re: Integrating Gaussians
- From: uunet!wri!keiper
- Date: Mon, 4 Jun 90 14:23:53 CDT
One way to trick Mathematica into evaluating Erf[] at infinities when the
sign of the argument is unknown is to do the following:
In[1]:= Unprotect[Erf]
Out[1]= {Erf}
In[2]:= Erf[DirectedInfinity[1] * ___] = 1
Out[2]= 1
In[3]:= Erf[DirectedInfinity[-1] * ___] = -1
Out[3]= -1
In[4]:= Integrate[Exp[-x^2/(2 sigma^2)],{x,-Infinity,Infinity}]
Out[4]= Sqrt[2] Sqrt[Pi] sigma
It will still be smart enough to figure out what to do with signed numbers:
In[5]:= Erf[DirectedInfinity[1] * (-2)]
Out[5]= -1
but if you have in mind a negative value for sigma it will give the wrong
answer.