Re: Simplification of definite integral?
- To: mathgroup at smc.vnet.net
- Subject: [mg40696] Re: [mg40673] Simplification of definite integral?
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Mon, 14 Apr 2003 04:00:50 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Mathematica has difficulties dealing with the (apparent) singularities
at x==d and x == -d so if you try straight forward Integrate it want's
you to assume that d non-real. However, you can get an answer probably
closer to what you desire by setting the PrincipalValue option to True:
Integrate[Sin[x-d]/(
x-d) Sin[x+d]/(x+
d),{x,-Infinity,Infinity},PrincipalValue->True,Assumptions->{d>0}]
(Pi*Cos[d]*Sin[d])/d
For example for d =1 we get:
%/.d->1.
1.42832
This is probably right, particularly that
NIntegrate[(Sin[x - 1]/(x - 1))*(Sin[x + 1]/(x + 1)),
{x, -Infinity, 1, Infinity}]
NIntegrate::slwcon:Numerical integration converging too slowly; suspect
one \
of the following: singularity, value of the integration being 0,
oscillatory \
integrand, or insufficient WorkingPrecision. If your integrand is
oscillatory \
try using the option Method->Oscillatory in NIntegrate.
NIntegrate::ncvb:NIntegrate failed to converge to prescribed accuracy
after 7 \
recursive bisections in x near x = 187.1757811919331`.
1.4283406894658994
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/
On Sunday, April 13, 2003, at 03:17 pm, Dr. Wolfgang Hintze wrote:
> How do I get a satisfactory result from mathematica for this function
>
> f[d]:=Integrate[Sin[x-d]/(x-d) Sin[x+d]/(x+d),{x,-Infinity,Infinity}]
>
> I tried
>
> f[d]//ComplexExpand
>
> and several assumptions but I didn't succeed. Any hints?
>
> Wolfgang
>
>
>
>