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MathGroup Archive 2007

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77598] Re: Re-defining Log over it's branch cut
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Wed, 13 Jun 2007 07:43:41 -0400 (EDT)
  • References: <f4dsng$hhu$1@smc.vnet.net>

Hi.

After Carl Woll's response I got back to your first question:

We have,

In[26]:=
Log[z] /. z -> r*Exp[0*I](*default of Mathematica; possitive axis,
above the cut*)

Out[26]=
Log[r]

In[27]:=
PowerExpand[Limit[Log[z], z -> r*Exp[e*I]]] /. e ->
        2*Pi(*positive axis, below the cut*)//InputForm

Out[27]//InputForm=
(2*I)*Pi + Log[r]

In[28]:=
PowerExpand[Limit[Log[z], z -> r*Exp[e*I]]] /. e -> -Pi(*negative
            axis, above the cut*)//InputForm

Out[28]//InputForm=
(-I)*Pi + Log[r]

In[29]:=
PowerExpand[Limit[Log[z], z -> r*Exp[e*I]]] /. e ->
        Pi(*negative axis, below the cut*)//InputForm

Out[29]//InputForm=
I*Pi + Log[r]

Dimitris



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