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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
>
>
>




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