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authorsiveshs <siveshs@gmail.com>2010-07-02 03:24:38 +0000
committerbnewbold <bnewbold@adelie.robocracy.org>2010-07-02 03:24:38 +0000
commitbd74caeb943c803ea175aed89e059e2fd6743781 (patch)
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parent4d5a5663e5983d2846f980d6cbb5ca2ae54a8706 (diff)
downloadafterklein-wiki-bd74caeb943c803ea175aed89e059e2fd6743781.tar.gz
afterklein-wiki-bd74caeb943c803ea175aed89e059e2fd6743781.zip
still testing
-rw-r--r--Fourier Series.page6
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@@ -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>