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