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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