Fourier { 2 if -2 < x < 0 ; 0 if 0 < x < 2}

The Fourier series expansion of f(x) is

where P = 4 is the period of f(x), and the coefficients are

(where k is a positive integer)

The series for f(x) reduces to

(I've attached a plot showing the original function in blue and the Fourier expansion with k = 10 terms)

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step-by-step explanation: