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author | siveshs <siveshs@gmail.com> | 2010-07-02 03:24:38 +0000 |
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committer | bnewbold <bnewbold@adelie.robocracy.org> | 2010-07-02 03:24:38 +0000 |
commit | bd74caeb943c803ea175aed89e059e2fd6743781 (patch) | |
tree | 6aedff0344ed3af418bf8c5ba47ee3727ba28fa9 | |
parent | 4d5a5663e5983d2846f980d6cbb5ca2ae54a8706 (diff) | |
download | afterklein-wiki-bd74caeb943c803ea175aed89e059e2fd6743781.tar.gz afterklein-wiki-bd74caeb943c803ea175aed89e059e2fd6743781.zip |
still testing
-rw-r--r-- | Fourier Series.page | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/Fourier Series.page b/Fourier Series.page index b603912..c90f37e 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -8,9 +8,9 @@ To show that Fourier series is plausible, let us consider some arbitrary trignom $$\begin{array}{ccl} e^{iy} = 1+iy+\frac{(iy)^{2}}{2!}+\frac{(iy)^{3}}{3!}+\frac{(iy)^{4}}{4!}+\frac{(iy)^{5}}{5!}+\cdots\\ - & = & 1+iy-\frac{y^{2}}{2!}-i\frac{y^{3}}{3!}+\frac{y^{4}}{4!}+i\frac{y^{5}}{5!}+\cdots\\ - & = & (1-\frac{y^{2}}{2!}+\frac{y^{4}}{4!}+\cdots)+i(y-\frac{y^{3}}{3!}+\frac{y^{5}}{5!}-\cdots)\\ - & = & \cos y+i\sin y\end{array}$$ + = 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}$$ ##What is the Fourier series actually?</b> |