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>
- Re: solving for a second function