       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

```

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