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authorsiveshs <siveshs@gmail.com>2010-07-02 03:26:30 +0000
committerbnewbold <bnewbold@adelie.robocracy.org>2010-07-02 03:26:30 +0000
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@@ -6,7 +6,7 @@ We first begin with a few basic identities on the size of sets. Show that the se
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:
$$
-\sin^2(x) & = & ?\\
+\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)\\