1. Show that formally Assume that a function f has a Fourier series nx L f(x)...

 

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1. Show that formally Assume that a function f has a Fourier series nπx L f(x) = Σ by sin n=1 ²[*Pr=[% L 2. Is there a corresponding result if f has a cosine series? explain and justify your answer 3. Apply the result of part (1) to the series for the sawtooth function f, and therefore show that 77² 6 2 = 1+ 1 1 22 32 0≤x≤L + 1 n² 71=1 where f is given by f(x) = x, -L < x < L, and f(-L) = f(L) = 0 and f is 2L periodic, that is f(x+2L) = f(x). 1. Show that formally Assume that a function f has a Fourier series nπx L f(x) = Σ by sin n=1 ²[*Pr=[% L 2. Is there a corresponding result if f has a cosine series? explain and justify your answer 3. Apply the result of part (1) to the series for the sawtooth function f, and therefore show that 77² 6 2 = 1+ 1 1 22 32 0≤x≤L + 1 n² 71=1 where f is given by f(x) = x, -L < x < L, and f(-L) = f(L) = 0 and f is 2L periodic, that is f(x+2L) = f(x).

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To ascertain the integral of The Fourier series of fx can be squared and the termbyterm integration ... View the full answer