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solving for a second function

• To: mathgroup at smc.vnet.net
• Subject: [mg102308] solving for a second function
• From: Roger Bagula <roger.bagula at gmail.com>
• Date: Wed, 5 Aug 2009 05:42:51 -0400 (EDT)

Yesterday I got an half Lemniscate complex function:
a = 1; b = 1;
f[t_] = (a*1 + b*I)/(a*1 + b*I*Exp[t]) - 1
FullSimplify[f[t]/f[t/2]]
gives:
(1 + 1/(Cosh[t/2] + I*Sinh[t/2]))
I want to solve for the other function:
g[t]/g[t/2]=(1 + 1/(-Cosh[t/2] + I*Sinh[t/2]))

Graphics showing this:x = Re[1 + 1/(Cosh[t] + I*Sinh[t])];
y = Im[1 + 1/(Cosh[t] + I*Sinh[t])];
z = x + I*y;
g1 = ParametricPlot[{x, y}, {t, -5*Pi, 5*Pi}, AspectRatio ->
Automatic]
(*The other half is: *)
x = Re[1 + 1/(-Cosh[t] + I*Sinh[t])];
y = Im[1 + 1/(-Cosh[t] + I*Sinh[t])];
z = x + I*y;
g0 = ParametricPlot[{x, y}, {t, -5*Pi, 5*Pi}, AspectRatio ->
Automatic]
Show[{g1, g0}]

Any help will be appreciated.
Roger Bagula

• Follow-Ups:
  • Re: solving for a second function
    • From: Daniel Lichtblau <danl@wolfram.com>