Re: Distinguished logarithm, branch cuts, etc.

*To*: mathgroup at smc.vnet.net*Subject*: [mg64939] Re: Distinguished logarithm, branch cuts, etc.*From*: "Alan" <info at optioncity.REMOVETHIS.net>*Date*: Wed, 8 Mar 2006 01:00:07 -0500 (EST)*References*: <duh2tv$5r3$1@smc.vnet.net> <dujrk0$8va$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

> You have to be careful here. 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 Thanks, Oleksandr. Unfortunately my z[u] spirals around the origin in the complex z-plane. So purely imaginary values are common. Here is a somewhat simplified example. Look at a parametric plot from u = 0 to u=10 for this z[u]: z[u] = f[u]/f[0], where f[u] = E^(20 (Sqrt[1/4 + (1 - rho^2) u^2 + I (rho - 1) u] - Sqrt[1-rho^2] u ) ), with say rho = -0.8. Any suggestions for this type of spiraling z[u]? regards, alan