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Re: Re-defining Log over it's branch cut

• To: mathgroup at smc.vnet.net
• Subject: [mg77507] Re: Re-defining Log over it's branch cut
• From: chuck009 <dmilioto at comcast.com>
• Date: Mon, 11 Jun 2007 04:21:14 -0400 (EDT)

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.

• Follow-Ups:
  • Re: Re: Re-defining Log over it's branch cut
    • From: Carl Woll <carlw@wolfram.com>