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