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MathGroup Archive 2000

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Re: Add the Logarithms (error in integral)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25205] Re: Add the Logarithms (error in integral)
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Fri, 15 Sep 2000 02:21:43 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <8p9j71$1fl@smc.vnet.net> <KGVu5.30316$Zh6.36755@ralph.vnet.net> <ozyv5.58213$Zh6.61667@ralph.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Jos R Bergervoet wrote:
> 
> Jens-Peer Kuska wrote:
> >
> > h1 = h //. a_.*Log[b_] + c_.*Log[d_] :> Log[b^a*d^c];
> >
> > Chop[N[h1 /. {a -> 10, b -> 10}]]
> >
> > 0.000716695
> 
> The trick seems interesting. But the answer is incorrect (for
> a=b=10 it must be ArcTan[50/Sqrt[101]], which is:

It is *not* a trick. The formulas can be found in Abramowitz/Stegun
4.1.7 -- 4.1.11

The condition for

Log[z1_]+Log[z2_] :> Log[z1*z2]  for -Pi < Arg[z1]+Arg[z2]<=Pi

and

n_.*Log[z_] :> Log[z^n]  for -Pi < Arg[n*z] <=Pi


it's clear that it is a bit complicated to fix these conditions
for a symbolic expression. The application is only save for real
arguments.

BTW: You ask for a *real* result and not for the correct real result ;-)

Regards
  Jens


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