Complex Function Plot

*To*: mathgroup at smc.vnet.net*Subject*: [mg25541] Complex Function Plot*From*: Roberto Brambilla <rlbrambilla at cesi.it>*Date*: Sat, 7 Oct 2000 03:35:44 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hi, dear MG-friends I have often to plot the real and the imaginary part of a complex valued function of a real variable : f(t). The obvious solution is Plot[{f[t]//Re,f[t]//Im},{t,t1,t2}, PlotStyle->{Hue[.7],Hue[.9]}] and the function is evaluated two times for each value of t. In the case of a long-time-eating function (as in the case of series expansions with hypergeometric f.,integrals with parameters,etc) it would be suitable a trick to evaluate f[t] only once. I'd like also to avoid to use interpolation like p=Table[f[t1+k(t2-t1)k/n],{k,0,n}]; fr=Interpolation[p//Re,InterpolationOrder->mr]; fi=Interpolation[p//Im,InterpolationOrder->mi]; Plot[{fr[t],fi[t]},{t,t1,t2}, PlotStyle->{Hue[.7],Hue[.9]}] since it requires the optimum choice of n, mr and mi for each (t1,t2) interval, especially if the two parts oscillate with very different periods. I use Math. version 3.0 . Any suggestion will be greatly appreciated. Bye, Rob Roberto Brambilla CESI Via Rubattino 54 20134 Milano tel +39.2.2125.5875 fax +39.2.2125.610 rlbrambilla at cesi.it