Summation of Fourier Series Problem: Plotting sm(x) for Multiple m Values

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SUMMARY

The discussion centers on plotting the Fourier Series expression

2/3 + (8/π²)∑(1/n²)(-1)ⁿcos(nπx/2)

for multiple values of

m

(5, 10, 20). The user seeks a computational tool to visualize the function

sm(x)

versus

x

, indicating a lack of software for this task. Recommendations include using

gnuplot

for generating the required plots.

PREREQUISITES

  • Understanding of Fourier Series and its components
  • Familiarity with mathematical notation and summation
  • Basic knowledge of plotting tools like gnuplot
  • Experience with numerical methods for function evaluation

NEXT STEPS

  • Research how to use

    gnuplot

    for plotting mathematical functions
  • Learn about Fourier Series convergence and its graphical representation
  • Explore alternative plotting libraries such as

    Matplotlib

    in Python
  • Investigate numerical methods for approximating series sums

USEFUL FOR

Students studying Fourier Series, mathematicians, and anyone interested in visualizing mathematical functions using computational tools.

Jamin2112
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Homework Statement



So, on a Fourier Series problem I came up with

2/3 + (8/π2)∑(1/n2)(-1)ncos(nπx/2)

I'm supposed to Plot sm(x) versus x for m= 5, 10, 20

(m is the index of the summation, which starts at m=1)



Homework Equations



meh


The Attempt at a Solution



The problem is that I don't have a computer program to do this. So I was wondering if someone could give me a link to a site that would do this.
 
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You might try looking up "gnuplot".
 

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