Question
In Problems, find the Fourier series of $f$ on the given interval.$$f(x)=\left\{\begin{array}{lr}0, & -\pi<x<0 \\e^{x}-1, & 0 \leq x<\pi\end{array}\right.$$
Step 1
The Fourier series of a function $f(x)$ is given by: $$f(x) = a_0 + \sum_{n=1}^{\infty} [a_n \cos(nx) + b_n \sin(nx)]$$ where $$a_0 = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) dx$$ $$a_n = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) \cos(nx) dx$$ $$b_n = \frac{1}{\pi} Show more…
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