Fourier series: Coefficients of Fourier series
Fourier series for even and odd functions: Step 1/3
Consider the #4#-periodic function #f# determined by
\[ f(x) = -2\cdot \cos \left({{\pi\cdot x}\over{4}}\right) \phantom{xx}\text{ for }\phantom{xx} -2 \le x\lt 2 \]
Enter a simplified expression for the Fourier coefficient \(a_0\), where the Fourier series of #f# is given by \[ s(x)=\frac{a_0}{2}+\sum_{m=1}^{\infty}\left(a_m\cdot\cos\left(\frac{m\cdot\pi\cdot x}{2}\right)+b_m\sin\left(\frac{m\cdot\pi\cdot x}{2}\right)\right)\]
\[ f(x) = -2\cdot \cos \left({{\pi\cdot x}\over{4}}\right) \phantom{xx}\text{ for }\phantom{xx} -2 \le x\lt 2 \]
Enter a simplified expression for the Fourier coefficient \(a_0\), where the Fourier series of #f# is given by \[ s(x)=\frac{a_0}{2}+\sum_{m=1}^{\infty}\left(a_m\cdot\cos\left(\frac{m\cdot\pi\cdot x}{2}\right)+b_m\sin\left(\frac{m\cdot\pi\cdot x}{2}\right)\right)\]
| \(a_0=\) |
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