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We’re working with this other differential equation just to make sure that we don’t get too locked into using one single differential equation. If you take the Fourier Transform of a specific exponential frequency with frequency term −ωo − ω o given as e−jωot e − j ω o t, the result is a single impulse at that frequency: δ(ω +ωo) δ ( ω + ω o). If k > 1, sinπ k ≠ 0. 0 2 Let f (x) for 0 < x <3, for 3 < 3 < 4. Sanfelici. I know that, for instance, if I have the following cosine series: f ( x) = ∑ n = 1 ∞ A n cos ( n π x L) The coefficients A n can be calculated by: A n = 2 L ∫ 0 L f ( x) cos ( n π x L) d x. Then the for loop ranges from the lower limit to the upper limit. Otherwise the product is said to diverge. By convention, the Fourier series is written as: f(t) ∼ a0 2 +∑n=1∞ an cos nπt +∑n=1∞ bn sin nπt f ( t) ∼ a 0 2 + ∑ n = 1 ∞ a n cos n π t + ∑ n = 1 ∞ b n sin n π t. 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