File:XCubed Fourier Series Approximation n=7,15.svg

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XCubed_Fourier_Series_Approximation_n=7,15.svg‎ (SVG file, nominally 720 × 460 pixels, file size: 83 KB)

Description

This is a graph of x3, periodic on (-π,π), with the Fourier Series Approximations drawn in at k=7 (red) and k=15 (blue). The approximation is given by

f\left( x \right) \approx \sum\limits_{n = 1}^k {{{ - 2\left( { - 1} \right)^n \left( {\pi ^2 n^2 - 6} \right)} \over {n^3 }}\sin \left( {nx} \right)} .

This is the counterpart to this, which has just the original function drawn in.
Date

22 February 2008(2008-02-22)
Source

Own Drawing, Plotted in Mathematica, edited in Inkscape.
Author

Inductiveload
Permission
(Reusing this image)
Public domain I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide.

In case this is not legally possible:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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Other versions image:XCubed Periodic (-pi, pi).svg

[edit] Mathematica Code

f[x_] = x^3;

ffour[x_, k_] =
  Hold[
   Sum[
    ((-2*(-1)^n*(Pi^2*n^2 - 6))/(n^3))*Sin[n*x],
    {n, 1, k}]
   ];

Plot[
 {f[Mod[x, 2 \[Pi], -\[Pi]]],
  ReleaseHold[ffour[x, 7]],
  ReleaseHold[ffour[x, 15]]},
 {x, -2 Pi, 2 Pi}]

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current02:29, 23 February 2008Thumbnail for version as of 02:29, 23 February 2008720×460 (83 KB)Inductiveload (Talk | contribs) ({{Information |Description= |Source= |Date= |Author= |Permission= |other_versions= }} )
02:00, 23 February 2008Thumbnail for version as of 02:00, 23 February 2008720×460 (83 KB)Inductiveload (Talk | contribs) ({{Information |Description= |Source= |Date= |Author= |Permission= |other_versions= }} )
01:21, 10 February 2007Thumbnail for version as of 01:21, 10 February 2007625×386 (189 KB)Inductiveload (Talk | contribs) ({{Information |Description=This is a graph of x<sup>3</sup>, periodic on (-π,π), with the Fourier Series Approximations drawn in at k=7 (red) and k=15 (blue). The approximation is given by <math>f\left( x \right) = \sum\limits_{n = 1}^k {{{ - 2\lef)

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