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Re: Integrating Gaussians

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

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