section 3 editing

1 files changed, 7 insertions, 2 deletions

diff --git a/Fourier Series.page b/Fourier Series.page
index 67b9027..430d536 100644
--- a/Fourier Series.page
+++ b/Fourier Series.page
@@ -78,7 +78,7 @@ Summing these two functions we get the following:
   
 <center>![$\cos^{2n}(x) + cos^{2n+1}(x)$](/cos10x-cos11x.gif)</center>
   
-#<b>What is the Fourier Series actually</b>
+#<b>What is the Fourier Series actually?</b>
 ##Initial Hypothesis
 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 : 
@@ -95,7 +95,12 @@ We begin proving this hypothesis by considering that any function on the right-h
   
 We now proceed to define certain operations on these functions in Hilbert space. One operation that will be particularly useful is that of the inner product of two functions:  
   
----> define inner product here
+$$
+\begin{array}{ccl}
+inner product, (f,g) & = & \int_0^{2\pi} f g dx\\
+\mid f \mid ^2 & = & (f, f) & = & \int_0^{2\pi} f^2 dx\\
+\end{array}
+$$
 
 This is the inner product of 2 real-number functions. For a function on complex numbers, the above definition must be altered as follows:    
 --> altered function here