diff options
Diffstat (limited to 'Fourier Series.page')
| -rw-r--r-- | Fourier Series.page | 2 |
1 files changed, 1 insertions, 1 deletions
diff --git a/Fourier Series.page b/Fourier Series.page index ae34c0f..ddcd3f4 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -121,7 +121,7 @@ In order to prove orthonormality of the basis vectors: $$ \begin{array}{ccl} -(f_n,f_m) = \int_0^{2\pi} \, \frac{1}{\sqrt{2\pi}} \, e^{inx} \, \longbar {\frac{1}{\sqrt{2\pi}} \, e^{inx}} \, dx\\ +(f_n,f_m) = \int_0^{2\pi} \, \frac{1}{\sqrt{2\pi}} \, e^{inx} \, \bar {\frac{1}{\sqrt{2\pi}} \, e^{inx}} \, dx\\ & = & \frac{1}{2\pi} \, \int_0^{2\pi} \, e^{i(n-m)x} \, dx \\ Here, n = m \Rightarrow (f_n,f_m) & = & 1\\ n \neq m \Rightarrow (f_n,f_m) & = & 0\\ |