Problem with Simplify and Integrating a gaussian
- To: mathgroup at smc.vnet.net
- Subject: [mg107935] Problem with Simplify and Integrating a gaussian
- From: David Weikersdorfer <weikersd at in.tum.de>
- Date: Wed, 3 Mar 2010 05:51:40 -0500 (EST)
Hello,
I encountered a very strange behaviour of Mathematica and would like to
ask if this is a bug or if I am doing something incredible wrong. I hope
this list is the right place to do so.
Please find below the contents of my notebook:
In[27]:= v[x_]=If[x<a,0,Exp[- ((x-a)/1.)^2]]
u[x_]=Simplify[v[x]]
Out[27]= If[x<a,0,Exp[-((x-a)/1.)^2]]
Out[28]= \[Piecewise]E^(-1. (a-1. x)^2) a<=x
0 True
In[29]:= Refine[Integrate[u[x],{x,d,\[Infinity]}],{d>a,a>0}]
Refine[Integrate[v[x],{x,d,\[Infinity]}],{d>a,a>0}]
Out[29]= 0.886227 (1.+Erf[a-1. d])
During evaluation of In[29]:= Refine::fas: Warning: One or more
assumptions evaluated to False. >>
Out[30]= 0.443113+0. E^(0. a^2) Erf[1. a]-0.443113 Erf[-1. a+1. d]
Hopefully this is not to obfuscated. The point is, that there is a
piecewise gaussian which I would like to Integrate. If I apply Simplify
and then call Integrate, I get a different result, than integrating
without calling Simplify. When "1." in In[27] is changed to "1",
Mathematica gives me a symbolic result which is correct for both u and v.
Kind Regards,
David