Work out the Fourier series of f, given over one period as follows.
At which values of x does the series fail to converge to f(x)? To what values does it converge at those points?
(h) |cos x| for all x
(k) x on 0<x<1, 1<x<2.
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Solution. By a theorem which states, if y=f(x) is a periodic function and y=f(x) is continuous at x=a, then its Fouries series converges to x=a; if y=f(x) is NOT continuous at x=b, then its Fouries series fails to converge to x=b. So,
(a) Its Fourier series converges to all points in and ...
Convergence of Fourier Series of Periodic Fuctions is investigated. The solution is detailed and well presented.