Fourier series: Coefficients of Fourier series
Fourier coefficients for arbitrary periods
Let #f# be the #30#-periodic function determined by #f(x)={{\pi^2\cdot x^2}\over{225}}# for #x\in \ivcc{-15}{15}#. You can use the fact that the Fourier series of the #2\pi#-periodic function #g# determined by #g(x)=x^2# for #x \in \ivcc{-\pi}{\pi}# is \[ \displaystyle \frac{\pi^2}{3} + \sum_{n=1}^{\infty} \frac{4}{n^2}(-1)^n \cos(nx)\]
Indicate which of the expressions below is the Fourier series of #f#.
Indicate which of the expressions below is the Fourier series of #f#.
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