Services & ResourcesWolfram ForumsMathGroup Archive

[Date Index] [Thread Index] [Author Index]

Re: Simplification of definite integral?

• To: mathgroup at smc.vnet.net
• Subject: [mg40698] Re: Simplification of definite integral?
• From: bobhanlon at aol.com (Bob Hanlon)
• Date: Mon, 14 Apr 2003 04:01:22 -0400 (EDT)
• References: <b7avdo$qlg$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

f[d_] := Evaluate[FullSimplify[
      Integrate[Sin[x-d]/(x-d) Sin[x+d]/(x+d),{x,-Infinity,Infinity}, 
        GenerateConditions->False]]]

f[d]

(Cos[2*d]*(Log[-(1/d)] - Log[1/d]))/(2*d)

f[d]//PowerExpand

(I*Pi*Cos[2*d])/(2*d)

Simplify[f[d], Element[d, Reals]&&d>0]

(I*Pi*Cos[2*d])/(2*d)


Bob Hanlon

In article <b7avdo$qlg$1 at smc.vnet.net>, "Dr. Wolfgang Hintze" <weh at snafu.de>
wrote:

<< Subject:	Simplification of definite integral?
From:		"Dr. Wolfgang Hintze" <weh at snafu.de>
To: mathgroup at smc.vnet.net
Date:		Sun, 13 Apr 2003 06:17:28 +0000 (UTC)

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 >><BR><BR>

• Follow-Ups:
  • Re: Re: Simplification of definite integral?
    • From: Dr Bob <majort@cox-internet.com>