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authorsiveshs <siveshs@gmail.com>2010-07-02 03:30:08 +0000
committerbnewbold <bnewbold@adelie.robocracy.org>2010-07-02 03:30:08 +0000
commit6d299375b982b107bb23d77a8b03cb987840ef20 (patch)
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downloadafterklein-wiki-6d299375b982b107bb23d77a8b03cb987840ef20.tar.gz
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@@ -5,12 +5,12 @@ 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:
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$\sin^2(x) = ?$
$\sin^2(x) = ?$
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$\sin^2(x) \tab = \tab ?$
->>>>>>> 1912254d86a8c3b7254873663aeb813e628d51d8
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$$\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)\\