Re: A FullSimplify Problem
- To: mathgroup at smc.vnet.net
- Subject: [mg41073] Re: [mg41050] A FullSimplify Problem
- From: Vladimir Bondarenko <vvb at mail.strace.net>
- Date: Thu, 1 May 2003 04:58:15 -0400 (EDT)
- In-reply-to: <200304300822.EAA25475@smc.vnet.net>
- References: <200304300822.EAA25475@smc.vnet.net>
- Reply-to: Vladimir Bondarenko <vvb at mail.strace.net>
- Sender: owner-wri-mathgroup at wolfram.com
"Ersek, Ted R" <ErsekTR at navair.navy.mil> wrote on Wednesday, April 30, 2003, 5:22:42 AM: ETR> At http://mathworld.wolfram.com/LeibnizIntegralRule.html ETR> I learned that ETR> Integrate[Log[1-2a Cos[x]+a^2],{x,0,Pi}] ETR> = 2*Pi*Log[Abs[a]] ETR> Mathematica knows how to do this integral, but gives a much more complicated ETR> result. Can anyone explain how to use FullSimplify and other ETR> transformations to show that the complicated result Mathematica gives is ETR> equivalent to the answer above? Actually, FullSimplify cannot do it as these answers are not identical ;-) For example, have a look at the plot. int = Integrate[Log[1 - 2a Cos[x] + a^2], {x, 0, Pi}]; answer = 2*Pi*Log[Abs[a]]; Plot[int - answer, {a, -1, 1}] and observe a curve which reminds y = 0 only very, very approximately :) Or, consider the following Integrate[Log[1 - 2(- 2I) Cos[x] + (- 2I)^2], {x, 0, Pi}] // N // Chop Integrate[Log[1 - 2a Cos[x] + a^2], {x, 0, Pi}] /. a -> - 2I // N NIntegrate[Log[1 - 2(- 2I) Cos[x] + (- 2I)^2], {x, 0, Pi}]//Chop 0 4.35517 - 9.8696 I 4.35517 I have added a CC to support at wolfram.com . You have an acute QA/QC flair... Pray, keep her steady. Viva la Cyber Tester! 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 ICQ : 173050619 Mail : 76 Zalesskaya Str, Simferopol, Crimea, Ukraine