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| author | siveshs <siveshs@gmail.com> | 2010-07-02 03:24:10 +0000 |
|---|---|---|
| committer | bnewbold <bnewbold@adelie.robocracy.org> | 2010-07-02 03:24:10 +0000 |
| commit | 4d5a5663e5983d2846f980d6cbb5ca2ae54a8706 (patch) | |
| tree | 0cbdc2d7d8de5d757ccb4d49efc44c32766b1cf4 | |
| parent | 3fbac26639134d806546c82626215c4bf4714385 (diff) | |
| download | afterklein-wiki-4d5a5663e5983d2846f980d6cbb5ca2ae54a8706.tar.gz afterklein-wiki-4d5a5663e5983d2846f980d6cbb5ca2ae54a8706.zip | |
still testing
| -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 a050d70..b603912 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -7,7 +7,7 @@ To show that Fourier series is plausible, let us consider some arbitrary trignom $1. \cos(2x) = 1 - 2 \sin^2(x)$ $$\begin{array}{ccl} -e^{iy} & = & 1+iy+\frac{(iy)^{2}}{2!}+\frac{(iy)^{3}}{3!}+\frac{(iy)^{4}}{4!}+\frac{(iy)^{5}}{5!}+\cdots\\ +e^{iy} = 1+iy+\frac{(iy)^{2}}{2!}+\frac{(iy)^{3}}{3!}+\frac{(iy)^{4}}{4!}+\frac{(iy)^{5}}{5!}+\cdots\\ & = & 1+iy-\frac{y^{2}}{2!}-i\frac{y^{3}}{3!}+\frac{y^{4}}{4!}+i\frac{y^{5}}{5!}+\cdots\\ & = & (1-\frac{y^{2}}{2!}+\frac{y^{4}}{4!}+\cdots)+i(y-\frac{y^{3}}{3!}+\frac{y^{5}}{5!}-\cdots)\\ & = & \cos y+i\sin y\end{array}$$ |