Re: Re: Re-defining Log over it's branch cut
- To: mathgroup at smc.vnet.net
- Subject: [mg77539] Re: [mg77507] Re: Re-defining Log over it's branch cut
- From: Carl Woll <carlw at wolfram.com>
- Date: Tue, 12 Jun 2007 01:25:30 -0400 (EDT)
- References: <200706110821.EAA20128@smc.vnet.net>
chuck009 wrote: >Hello Dimitris, > >Is there a way to have Mathematica do this substitution internally when evaluating powers such as z^s? The reason I ask is that I'm working on the contour integral expressions for Zeta and Polylog which use the Hankel contour. This contour requires the substitutions z=rExp[pi i] and z=r Exp[-pi i]. However, Mathematica assigns the "standard convention" of pi to the argument for both cases. For example if I specify: > >In[248]:= >N[z^(s-1)/.z->r Exp[-Pi I]] > >Mathematica return an answer that is actually: > >Exp[(s-1)(Log[r]+pi i] > >and not: > >Exp[(s-1)(Log[r]-pi i] > > >I realize that's the standard convention. Just would make my code a little less messy if I didn't have to do the expansion myself and "manually" insert the -pi i factor. > > One possibility is to use Limit: In[45]:= Limit[z^(s - 1) /. z -> r Exp[-I (Pi - eps)], eps -> 0, Assumptions -> r > 0] Out[45]= E^((-1 + s)*((-I)*Pi + Log[r])) Carl Woll Wolfram Research
- References:
- Re: Re-defining Log over it's branch cut
- From: chuck009 <dmilioto@comcast.com>
- Re: Re-defining Log over it's branch cut