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MathGroup Archive 2004

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RE: proof of formula for log(-t) found in Mathematica?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48281] RE: [mg48194] proof of formula for log(-t) found in Mathematica?
  • From: "Dr A.H. Harker" <a.harker at ucl.ac.uk>
  • Date: Fri, 21 May 2004 03:54:29 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

 Is it really built into Mathematica? Certainly V5.0, given
Log[-t] == Log[t^2]/2 + I*Arg[-t]
does not return True. Which is just as well, as t^2 and the square
modulus of t are not the same (unless t happens to be real). 

 Dr A.H. Harker
 Director of Postgraduate Studies
 Deputy Head, Condensed Matter and Materials Physics Group
 Department of Physics and Astronomy
 University College London
 Gower Street
 LONDON
 WC1E  6BT
 (44)(0)207 679 3404
 a.harker at ucl.ac.uk


-----Original Message-----
From: Roger L. Bagula [mailto:rlbtftn at netscape.net] 
To: mathgroup at smc.vnet.net
Subject: [mg48281] [mg48194] proof of formula for log(-t) found in Mathematica?

I found this while doing work on complex exponents:

f(t)=Log[-t]=Log[t^2]/2+I*Arg[-t]

It is a result built into Mathematica.
I would like to see how it is derived as it seem counter intuitive in 
it's results.
Respectfully,
Roger L. Bagula



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