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author | siveshs <siveshs@gmail.com> | 2010-07-02 22:58:52 +0000 |
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committer | bnewbold <bnewbold@adelie.robocracy.org> | 2010-07-02 22:58:52 +0000 |
commit | 39f742738378e1679b9bb620fa7bbaf1652a1a6b (patch) | |
tree | 6f6bc017bffb39a7d1e6702de3c7631613fd962c | |
parent | ed7054dbf0bad7b6d916cbe2bc996687d89be4c5 (diff) | |
download | afterklein-wiki-39f742738378e1679b9bb620fa7bbaf1652a1a6b.tar.gz afterklein-wiki-39f742738378e1679b9bb620fa7bbaf1652a1a6b.zip |
section 2 editing
-rw-r--r-- | Fourier Series.page | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/Fourier Series.page b/Fourier Series.page index f084674..041a83a 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -72,10 +72,10 @@ As a final test to see if the Fourier series really could exist for any periodic If it is possible to approximate the above function using a sum of sines and cosines, then it can be argued that *any* continuous periodic function can be expressed in a similar way. This is because any function could be expressed as a number of peaks at every position. -It turns out that the above function can be approximated as the sum of two cosines, namely, $\cos^{2n}(x) + cos^{2n+1}(x)$ +It turns out that the above function can be approximated as the difference of two cosines, namely, $\cos^{2n}(x) + cos^{2n+1}(x)$ <center>![$\cos^{2n}(x)$](/cos10x.gif) ![$cos^{2n+1}(x)$](/cos11x.gif) </center> Summing these two functions we get the following: -![$\cos^{2n}(x) + cos^{2n+1}(x)$(/cos10x-cos11x.gif) +![$\cos^{2n}(x) + cos^{2n+1}(x)$](/cos10x-cos11x.gif) ##What is the Fourier series actually?</b> |