Find the Fourier series representation of f(x) in the interval [−π, π]: f(x)=egin{cases}0,&-pi<xle 0\sin x,&0<xlepiend{cases}. Hence show that sum_{n=1}^inftyfrac{1}{4n^2-1}= frac{1}{2}.
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The Fourier series of a function f(x) in the interval [0,T] is given by: f(x) = a0/2 + Σ [an cos(2πnx/T) + bn sin(2πnx/T)] where the coefficients an and bn are given by: an = (2/T) ∫_0^T f(x) cos(2πnx/T) dx bn = (2/T) ∫_0^T f(x) sin(2πnx/T) dx For f(x) = Show more…
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