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 A Fourier series is a function of the form $\sum_{n=-\infty}^\infty a_n e^{inx}$ or $\sum_{n=-\infty}^\infty b_n \cos(n x) + c_n \sin (n x)$, depending on one's taste for the imaginary. The rumor on the street is that any periodic function (well, any nice one) can be expressed as a Fourier series: you hand me a function $f:[0,2\pi]\rightarrow \mathbb{C}$ and I hand you a list of real numbers $b_0,c_0,b_1,c_1,b_2,c_2,b_3,c_3,\dots$ such that
 
-$f(x) = \sum_{n=-\infty}^\infty b_n \cos(n x) + c_n \sin (n x).$
+$$f(x) = \sum_{n=-\infty}^\infty b_n \cos(n x) + c_n \sin (n x).$$
 
 If this exchange is always possible, there must be at least as many different lists of real numbers as there are nice periodic functions. So how many are there of each?