I tried to to fourier series for $f(x) = \cos(3x)$, and I keep getting $0$ for all coeficients, $a_0$ and $a_n$. Am I missing something? Could $\cos(3x)$ be fourier series on its own?
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4I don't get it. This is like asking for Taylor series of $x^3$. A Fourier series is a sum of sines and cosines with integer multiples of some fundamental frequency. Can you show your work? – A. Thomas Yerger Feb 03 '24 at 17:33
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I found this question in old russian book. Precise question goes: Find fourier series of function $f(x) = \cos(3x)$ on $(-\pi, \pi)$ – murat Feb 03 '24 at 17:36
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2$\cos(3x)$ is its own Fourier series. – K.defaoite Feb 03 '24 at 17:44
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Or do you want $f(x) = \frac12 e^{-3xi} + \frac12 e^{3xi}$? – peterwhy Feb 03 '24 at 18:02