Re: proof of formula for log(-t) found in Mathematica?
- To: mathgroup at smc.vnet.net
- Subject: [mg48219] Re: proof of formula for log(-t) found in Mathematica?
- From: Erich Neuwirth <erich.neuwirth at univie.ac.at>
- Date: Tue, 18 May 2004 04:16:46 -0400 (EDT)
- References: <firstname.lastname@example.org>
- Sender: owner-wri-mathgroup at wolfram.com
Well, if |t|=1, then the formula is Log[-t]=I*Arg[-t] which is the same as -t=Exp[I*Arg[-t]] which is the definition of Arg Log[t^2]/2=Log[|t|], which you have to add if |t|!=1, so the formula is correct since Log[-t]=Log[|-t|*Exp[i*Arg[-t]]=Log[[-t|]+Log[Exp[I*Arg[-t]]= Log[|t|]+I*Atg[-t]=Log[t^2]/2+I*Atg[-t] Roger L. Bagula wrote: > 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 >