Re-defining Log over it's branch cut

*To*: mathgroup at smc.vnet.net*Subject*: [mg77458] Re-defining Log over it's branch cut*From*: chuck009 <dmilioto at comcast.com>*Date*: Sat, 9 Jun 2007 05:33:56 -0400 (EDT)

Hello all, When integrating along a logarithmic branch cut, often have to define two values of z: z=r Exp[0 i] which is a path above the positive real axis z=r Exp[2 pi i] which is the path below the positive real axis However, when I make a transformation rule: Log[z] /.z->r Exp[0 i] returns Log[r] but: Log[z] /.z->r Exp[2 pi i] should be Log[r]+2 pi i however Mathematica returns Log[r] in both cases. Is there a way to configure the Log function to return these two values? I have the same question when the branch cut is along the negative real axis: Log[z] /. z->r Exp[-pi i] (needs to be Log[r]-pi i) Log[z] /. z->r Exp[pi i] (needs to be Log[r]+pi i)