From b8fe1b1c707ebd1a6c92fc8fbe88f476eac57991 Mon Sep 17 00:00:00 2001 From: joshuab <> Date: Thu, 8 Jul 2010 02:56:45 +0000 Subject: formatting --- ClassJune28.page | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/ClassJune28.page b/ClassJune28.page index 2190bb7..2a7065f 100644 --- a/ClassJune28.page +++ b/ClassJune28.page @@ -6,7 +6,7 @@ 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? -- cgit v1.2.3