Re: natural log of E
- To: mathgroup at christensen.cybernetics.net
- Subject: [mg2017] Re: natural log of E
- From: wagner at bullwinkle.cs.Colorado.EDU (Dave Wagner)
- Date: Thu, 14 Sep 1995 23:29:11 -0400
- Organization: University of Colorado, Boulder
In article <DEKnts.Avv at wri.com>, > >I suspect that the reason that Mathematica is not able to >interpret "Log[E^n]" as "n" might have to do with the fact that >"Log" is a multivalued function of its argument, and Mathematica >isn't able to decide on which Riemann sheet to put the answer. >However, this isn't an entirely satisfactory answer, since when I >ask for "Log[E]", mm spits out "1" rather than "1 + 2 Pi I n_Integer" >or somesuch. /*shrug*/ Beats me. I guess that's a question for >the experts. ComplexExpand[Log[Exp[n]]] returns n. The following command, which tells ComplexExpand to treat n as a complex number, reflects the multi-valued aspect of the Log function (albeit by expressing the result in terms of another multi-valued function, ArcTan). In[5]:= ComplexExpand[Log[Exp[n]], n] Out[5]= I ArcTan[Cos[Im[n]], Sin[Im[n]]] + Re[n] Dave Wagner Principia Consulting (303) 786-8371 dbwagner at princon.com http://www.princon.com/princon