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Redefining Log over it's branch cut
 To: mathgroup at smc.vnet.net
 Subject: [mg77458] Redefining 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)
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