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authorsiveshs <siveshs@gmail.com>2010-07-02 22:58:52 +0000
committerbnewbold <bnewbold@adelie.robocracy.org>2010-07-02 22:58:52 +0000
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@@ -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>