section 3 editing

1 files changed, 8 insertions, 1 deletions

diff --git a/Fourier Series.page b/Fourier Series.page
index e339854..c764b6a 100644
--- a/Fourier Series.page
+++ b/Fourier Series.page
@@ -159,7 +159,14 @@ $$
   
 Extending this principle to the case of an n-dimensional vector:  
   
-Let  $f$ be the periodic function expressed as $f= \Sigma a_n \frac{1}{\sqrt{2\pi}} \, e^{inx} = \Sigma a_n \, f_n$ where $a_n \in \mathbb C$
+Let  $f$ be the periodic function expressed as $f= \Sigma a_n \frac{1}{\sqrt{2\pi}} \, e^{inx} = \Sigma a_n \, f_n$ where $a_n \in \mathbb C$ and $f_n$ are the basis vectors.  
+
+Inner product of the vector (in this case the function $f$) with the some basis vector $f_m$ is:
+$$
+\begin{array}{ccl}
+(f, f_m) & = & \left( \Sigma a_n\,f_n , f_m \right)\\
+& = & \Sigma a_n\,\left(f_n , f_m \right)\\
+
 
 ##Proving that this function is does indeed completely represent $f$