Homework #10 Due: Thursday, April 29, 2010 Note: Use of Matlab (or any other software) is not permitted. I.(see Exercise 4.2) Use Poisson’s relation to find the Fourier series for each of the following p-periodic functions on R: a.(1pt) ∑∞−∞=−−=mmpxexf2)()(πb.(1pt) ∑∞−∞=−−=mmpxaexf||)(,a>0II.(see Exercise 4.10) Let f be a suitably regular 1-periodic function, let 0<x0<1, and let mbe a positive integer m=1,2,3,… What can you infer about the Fourier coefficients (cn)nof fif you know that: a.(1pt) )()(xfxf=b.(1pt) )()(xfxf−=c.(1pt) )(1xfmxf=⎟⎠⎞⎜⎝⎛+d.(1pt) )(21xfxf−=⎟⎠⎞⎜⎝⎛+e.(1pt) ())(00xxfxxf−=+f.(1pt)
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