Re: Incorrect symbolic improper integral
- To: mathgroup at smc.vnet.net
- Subject: [mg103611] Re: [mg103586] Incorrect symbolic improper integral
- From: Leonid Shifrin <lshifr at gmail.com>
- Date: Wed, 30 Sep 2009 05:00:21 -0400 (EDT)
- References: <200909291138.HAA25632@smc.vnet.net>
A follow - up to my previous post:
1. Of course, the simple form of the answer I gave is just
Pi*Exp[-Abs[a]]
2. When I was talking about pole contributions, I meant for two
exponential terms Exp[I*a*x] and Exp[-I*a*x] (expanding the cosine)
separately. The two terms always pick the opposite poles but give
the same contribution. The single term never gets the contribution from
both poles.
Regards,
Leonid
On Tue, Sep 29, 2009 at 4:38 AM, jwmerrill at gmail.com <jwmerrill at gmail.com>wrote:
> Below is a definite integral that Mathematica does incorrectly.
> Thought someone might like to know:
>
> In[62]:= Integrate[Cos[x]/(1 + x^2), {x, -\[Infinity], \[Infinity]}]
>
> Out[62]= \[Pi]/E
>
> What a pretty result--if it were true. The correct answer is \[Pi]*Cosh
> [1], which can be checked by adding a new parameter inside the
> argument of Cos and setting it to 1 at the end:
>
> In[61]:= Integrate[Cos[a x]/(1 + x^2), {x, -\[Infinity], \[Infinity]},
> Assumptions -> a \[Element] Reals]
>
> Out[61]= \[Pi] Cosh[a]
>
> Regards,
>
> Jason Merrill
>
>
- References:
- Incorrect symbolic improper integral
- From: "jwmerrill@gmail.com" <jwmerrill@gmail.com>
- Incorrect symbolic improper integral