Plotting a series using gnuplot (Maclaurin series)

0
votes

Is there a quick way to plot the Maclaurin/Taylor series using Gnuplot. For eg: http://en.wikipedia.org/wiki/Power_series I'm trying to plot each term of the series NOT the series f(x) vs x. So, for sin(x) I'd like to plot on the x-axis, x, -x^3/3!, x^5/5! etc and the sum itself all on one axis without having to type each term in the sequence manually.

1
gnuplot
I don't want to plot each term manually. - user621819

1 Answers

1
votes

You can plot functions in gnuplot. In this case, you would have to define your series, for example: 

gnuplot> a0 = 1
gnuplot> a1 = 0.5
gnuplot> a2 = 0.1
gnuplot> f(x) = a0 + a1*x**2 + a2*x**3
gnuplot> plot f(x)

This will give you:

plot series

Edit

Based on the comment to this answer, I'm proposing this (which should work for gnuplot 4.4 and higher):

First, define your factorial:

gnuplot> fac(n) = (n==0) ? 1 : n * fac(n-1)

Second, iterate over as many terms as you like (in this case 10). We're only interested in the uneven exponents, hence the upper bound is 20. Furthermore, every other "term" has to be multiplied by -1, thus two commands, and an increment of 4: 

plot for [a=3:21:4] -1*x**a/fac(a), for [a=1:21:4] x**a/fac(a)

This will give you a plot like this:

plot terms