Re: Simplification of definite integral?
- To: mathgroup at smc.vnet.net
- Subject: [mg40758] Re: Simplification of definite integral?
- From: "Steve Luttrell" <luttrell at _removemefirst_westmal.demon.co.uk>
- Date: Wed, 16 Apr 2003 01:37:24 -0400 (EDT)
- References: <200304130617.CAA27308@smc.vnet.net> <b7dq00$67a$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Your result is correct, but why is PrincipalValue needed for a non-singular integrand? I got the wrong answer earlier - I should have checked it numerically! -- Steve Luttrell West Malvern, UK "Vladimir Bondarenko" <vvb at mail.strace.net> wrote in message news:b7dq00$67a$1 at smc.vnet.net... > 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?