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Diffstat (limited to 'Fourier Series.page')
| -rw-r--r-- | Fourier Series.page | 7 |
1 files changed, 4 insertions, 3 deletions
diff --git a/Fourier Series.page b/Fourier Series.page index cb19358..ff1449e 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -84,7 +84,7 @@ Let $f : \mathbb I \rightarrow \mathbb C$ be a continuous, periodic function whe $$ \begin{array}{ccl} -f & = & \Sigma e^{inx}\\ +f & = & \Sigma a_n \, e^{inx}\\ & = & a_0 + \Sigma a_n\cos nx + \Sigma b_n\sin nx\\ \end{array} $$ @@ -157,8 +157,9 @@ $$ \end{array} $$ -Extending this principle to the case of an n-dimensional vector: ---> compute inner product here and then continue to show what the coefficient formula is +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 $a_n \Epsilon \mathbb C$ ##Proving that this function is does indeed completely represent $f$ |