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MathGroup Archive 1990

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Re: Gaussians

  • To: mathgroup at yoda.ncsa.uiuc.edu
  • Subject: Re: Gaussians
  • From: uunet!cod.nosc.mil!marchett (David J. Marchette)
  • Date: Mon, 4 Jun 90 21:58:07 PDT

Thanks again for all those who responded to my query.  Here is the
simplest solution: (Type the following into mathematica)

f[x_,s_] := Exp[-(x/s)^2/2]/(Sqrt[2 Pi] s)

Unprotect[Erf]
Erf[DirectedInfinity[1] * ___] = 1
Erf[DirectedInfinity[-1] * ___] = -1
Protect[Erf]

Integrate[f[x,sigma],{x,-Infinity,Infinity}]

(* Yay! *)

Integrate[f[x,sigma]^2,{x,-Infinity,Infinity}]

(* Yay! *)

Integrate[f[x,sigma1] f[x,sigma2],{x,-Infinity,Infinity}]

(* Boo! *)

As you can see, if you did the above, it's still hosed.  Now it seems that
I need to tell it that Sqrt[-x] I is -Sqrt[x], and whatall. It is pretty clear
that in order to do what I want, I have to know much more about Mathematica.
Does anyone out there have access to Macsyma or Maple?  Do these also
choke on this?  I'm not saying that Mathematica is wrong, mind you, it's
just not giving me what I want.  Am I too demanding?

By the way, I apologize for not providing Mathematica output.  My email and
Mathematica are on different machines, and the networking is at 1200 baud over
the phone lines (networked into the 50s we call it).  If I come up with any
really complicated questions, I'll figure out a way to get the full session.

David Marchette
marchett at nosc.mil



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