Re: Simplification of definite integral?
- To: mathgroup at smc.vnet.net
- Subject: [mg40719] Re: Simplification of definite integral?
- From: "Dr. Wolfgang Hintze" <weh at snafu.de>
- Date: Tue, 15 Apr 2003 03:56:48 -0400 (EDT)
- References: <200304130617.CAA27308@smc.vnet.net> <b7dq00$67a$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Vladimir,
that's exactly what I was looking for. I new the result beforehand. I
didn't want to go through Fourier transforms.
I observed the the main part of the work is being done by adding (none
of which can be removed)
(1) Assumptions -> d>0 and
(2) PrincipalValue -> True
which already gives
Pi * Cos[d] Sin[d] / d
I'm rather new to mathematica. And my first impression is that part of
the "art of mathematica" seems to be to guess which might be the answer
and then to find the appropriate simplification mechanisms by hand.
Thanks again
Kind regards
Wolfgang Hintze, Berlin
Vladimir Bondarenko wrote:
> Sunday, April 13, 2003, 3:17:27 AM, "Dr. Wolfgang Hintze" <weh at snafu.de> wrote:
>
> DWH> How do I get a satisfactory result from mathematica for this function
>
> DWH> f[d]:=Integrate[Sin[x-d]/(x-d) Sin[x+d]/(x+d),{x,-Infinity,Infinity}]
>
> DWH> I tried
>
> DWH> f[d]//ComplexExpand
>
> DWH> and several assumptions but I didn't succeed. Any hints?
>
>
> I am not sure of what is 'a satisfactory result'? Do you mean something
> like this
>
> Integrate[Sin[x - d]/(x - d) Sin[x + d]/(x + d), {x, -Infinity, Infinity},
> Assumptions -> d > 0, PrincipalValue -> True]//TrigReduce
>
> (Pi*Sin[2*d])/(2*d)
>
>
> ?
>
>
> Best wishes,
>
> Vladimir Bondarenko
> Mathematical and Production Director
> Symbolic Testing Group
>
> Web : http://www.CAS-testing.org/ GEMM Project (95% ready)
> Email: vvb at mail.strace.net
> Voice: (380)-652-447325 Mon-Fri 6 a.m. - 3 p.m. GMT
> Mail : 76 Zalesskaya Str, Simferopol, Crimea, Ukraine
>
>
>
>
- References:
- Simplification of definite integral?
- From: "Dr. Wolfgang Hintze" <weh@snafu.de>
- Simplification of definite integral?