How to Plot a Series

Question

I would like to plot

f1[x_, n_] := Sum[Sin[(2 j - 1) x]/(2 j - 1), {j, 1, n}]

on a single plot containing f1(x,50), f1(x,100), f1(x,1000), with three different colored lines.

Please help

Yes, j and k and equal. I must've input k instead of j at the end — Curious14, Oct 1, 2014 at 22:42

kglr · Accepted Answer · 2014-10-01 22:44:43Z

3

f1[x_, n_] := Sum[Sin[(2 j - 1) x]/(2 j - 1), {j, 1, n}]; 
Plot[ f1[x, #] & /@ {50, 100, 1000}, {x, -Pi, Pi}, Evaluated -> True]

enter image description here

answered Oct 1, 2014 at 22:44

kglr

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$\begingroup$ Can you help me to understand what the input "f1[x, #] & /@ {50, 100, 1000}" means? Specifically the "#" and "& /@" $\endgroup$
– Curious14
Oct 1, 2014 at 22:47
1

$\begingroup$ @MathStudent, f1[x, #] & /@ {50, 100, 1000} is shorter way of writing {f1[x, 50],f1[x,100],f1[x,1000]}. See docs on Slot (#) and Map (/@) $\endgroup$
– kglr
Oct 1, 2014 at 22:49
$\begingroup$ Nice plot, it shows the Gibbs phenomenon clearly. $\endgroup$
– xslittlegrass
Oct 1, 2014 at 22:52
$\begingroup$ Thank you for the clarification! $\endgroup$
– Curious14
Oct 1, 2014 at 22:56

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Mahdi · Accepted Answer · 2014-10-01 22:47:29Z

2

Assuming that this the correct function:

f1[x_, n_] := Sum[Sin[(2 k - 1) x]/(2 k - 1), {k, 1, n}];

We can plot them by the following command:

Plot[f1[x, #] & /@ {50, 100, 1000}, {x, 0, Pi}, PlotLegends -> Placed[{"50", "100", "1000"}, {1.01, 0.5}]]

or equivalently:

Plot[{f1[x,50],f1[x,100],f1[x,1000]}, {x, 0, Pi}, PlotLegends -> Placed[{"50", "100", "1000"}, {1.01, 0.5}]]

for 0 to $\pi$.

enter image description here

answered Oct 1, 2014 at 22:47

Mahdi

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$\begingroup$ Your second plotting input is much easier to understand, where you commanded each of the plots. May you help me to understand what "{1.01, 0.5}" means? $\endgroup$
– Curious14
Oct 1, 2014 at 22:51
$\begingroup$ Yes! I use Placed command to put the legend at {1.01,0.5}. Mathematica assumes that the figure coordinates is {0,1} horizontally and vertically. So for example if write {0.5,0.5} legend will be right at the middle of figure. $\endgroup$
– Mahdi
Oct 1, 2014 at 23:09

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2 Answers 2