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author | Nao Pross <naopross@thearcway.org> | 2020-10-06 17:38:31 +0200 |
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committer | Nao Pross <naopross@thearcway.org> | 2020-10-06 17:38:31 +0200 |
commit | 8f9b3b5be58c6f49a1392edcc902d4dd00a8a7a8 (patch) | |
tree | caebb4c8a31162c5d20ff8144bc4ed21ec50dac8 /komfour_zf.tex | |
parent | Add complex representation of fourier coefficients (diff) | |
download | KomFour-master.tar.gz KomFour-master.zip |
Diffstat (limited to 'komfour_zf.tex')
-rw-r--r-- | komfour_zf.tex | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/komfour_zf.tex b/komfour_zf.tex index 485eb1e..cc42a1d 100644 --- a/komfour_zf.tex +++ b/komfour_zf.tex @@ -462,11 +462,11 @@ \begin{theorem}[Fourier coefficients of even and odd functions] Recall that a function is said to be \emph{even} if \(f(-x) = f(x)\) or \emph{odd} if \(f(-x) = -f(x)\). We can show that if a function is \begin{itemize} - \item odd, then \(b_n = 0\) for all \(n\), and + \item even, then \(b_n = 0\) for all \(n\), and \[ a_n = \frac{4}{T}\int\limits_0^{T/2} f(t)\cos(n\omega t)\di{t} \] - \item even, then \(a_n = 0\) for all \(n\), and + \item odd, then \(a_n = 0\) for all \(n\), and \[ b_n = \frac{4}{T}\int\limits_0^{T/2} f(t)\sin(n\omega t)\di{t} \] |