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| author | joshuab <> | 2010-07-08 02:56:45 +0000 |
|---|---|---|
| committer | bnewbold <bnewbold@adelie.robocracy.org> | 2010-07-08 02:56:45 +0000 |
| commit | b8fe1b1c707ebd1a6c92fc8fbe88f476eac57991 (patch) | |
| tree | 94da441917f18635bd56530e8a6ee7ea485c62f2 /ClassJune28.page | |
| parent | f4c035e1e4969e36e507dfa8b35a98a2564f95ff (diff) | |
| download | afterklein-wiki-b8fe1b1c707ebd1a6c92fc8fbe88f476eac57991.tar.gz afterklein-wiki-b8fe1b1c707ebd1a6c92fc8fbe88f476eac57991.zip | |
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| -rw-r--r-- | ClassJune28.page | 2 |
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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? |