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| author | siveshs <siveshs@gmail.com> | 2010-07-02 03:26:16 +0000 |
|---|---|---|
| committer | bnewbold <bnewbold@adelie.robocracy.org> | 2010-07-02 03:26:16 +0000 |
| commit | 2244db2d573301f10baaa36b81a5892087613ffd (patch) | |
| tree | 1d0970503a6a1bc1a8a8b9f893b54f788fba200f | |
| parent | f12ef31ef71c32ff3a8071595cf27eff4322477d (diff) | |
| download | afterklein-wiki-2244db2d573301f10baaa36b81a5892087613ffd.tar.gz afterklein-wiki-2244db2d573301f10baaa36b81a5892087613ffd.zip | |
still testing
| -rw-r--r-- | Fourier Series.page | 3 |
1 files changed, 2 insertions, 1 deletions
diff --git a/Fourier Series.page b/Fourier Series.page index fb9ed7e..efa2b85 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -5,8 +5,9 @@ We first begin with a few basic identities on the size of sets. Show that the se ##Why Fourier series is plausible?</b> To show that Fourier series is plausible, let us consider some arbitrary trignometric functions and see if it is possible to express them as the sum of sines and cosines: -$$\begin{array}{ccl} +$$ \sin^2(x) & = & ?\\ +\begin{array}{ccl} & = & 1+iy-\frac{y^{2}}{2!}-i\frac{y^{3}}{3!}+\frac{y^{4}}{4!}+i\frac{y^{5}}{5!}+\cdots\\ & = & (1-\frac{y^{2}}{2!}+\frac{y^{4}}{4!}+\cdots)+i(y-\frac{y^{3}}{3!}+\frac{y^{5}}{5!}-\cdots)\\ & = & \cos y+i\sin y\end{array}$$ |