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authorsiveshs <siveshs@gmail.com>2010-07-03 03:33:37 +0000
committerbnewbold <bnewbold@adelie.robocracy.org>2010-07-03 03:33:37 +0000
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@@ -79,8 +79,9 @@ Summing these two functions we get the following:
<center>![$\cos^{2n}(x) + cos^{2n+1}(x)$](/cos10x-cos11x.gif)</center>
#What is the Fourier series actually?</b>
+
Now, to prove that the Fourier series is indeed true, we begin with the following hypothesis:
-Let $f : \mathbb I \rightarrow \mathbb C$ be a continuous, periodic function where $I$ is some time interval(period of the function). Then it can be expressed as :
+Let $f : \mathbb I \rightarrow \mathbb C$ be a continuous, periodic function where $I$ is some time interval(period of the function). Then it can be expressed as :
$$
\begin{array}{ccl}