Re: Distinguished logarithm, branch cuts, etc.
- To: mathgroup at smc.vnet.net
- Subject: [mg64904] Re: Distinguished logarithm, branch cuts, etc.
- From: "sashap" <pavlyk at gmail.com>
- Date: Tue, 7 Mar 2006 06:11:55 -0500 (EST)
- References: <email@example.com>
- Sender: owner-wri-mathgroup at wolfram.com
You have to be careful here. An analytic function like BesselI[ nu, z ] *is* a continuous map from complex plane to a multi-sheeted Riemann surface. It is when you project from this Riemann surface, branch-cuts appear. It seems that your problem would benefit from the branch-cut convention different from the one adopted in Mathematica. Provided z[u] can never take on purely imaginary values possible modification could be (z[u]^2)^(nu/2)*BesselI[nu, z[u]]/(z[u])^nu or equivalently BesselI[nu, Sqrt[ z[u]^2] ] Oleksandr Pavlyk Wolfram Research