Integration or Evaluation Bug
- To: mathgroup at smc.vnet.net
- Subject: [mg69339] Integration or Evaluation Bug
- From: "Chris H. Fleming" <chris_h_fleming at yahoo.com>
- Date: Thu, 7 Sep 2006 23:58:06 -0400 (EDT)
I have found what is either a bug in integration or evaluation of
exponential integrals and boiled it down to this simple example
NIntegrate[Exp[-w] Cos[w t] / (w^2+1),{w,0,1000}]
Plotted as a function of t, this is correctly oscillatory decay
Assuming[t > 1/1000, Integrate[Exp[-w] Cos[w t] / (w^2+1),{w,0,1000}]]
Plotted as a function of t, this is incorrectly growth instead of
decay.
The analytic answer has all terms like Exp[stuff t] Ei[-stuff t]
If stuff was real, that would decay like 1/(stuff t)
So I don't know if it's an integration bug or a bug in Ei evaluation