Question

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We did not include a normalizing factor in (8.11), so Ilpk 112-2π and the Fourier coefficients of an integrable function f E L1 (T) are defined by 2π (8.12) -ikx 2nJ_π 8.2 For xe (0, π), let g(x) = x (a) Extend g to an even function on T and compute the periodic Fourier coeffi cients clg] according to (8.12). (Note that the case k = 0 needs to be treated separately.) Show that the periodic series reduces to a cosine series in this case.

Answer 1

a ti al ike ik i Kn -T) e -TK -Te (K)

Fo even ㄒㄒ- ㄧ Cke ion and We an even umeti @rリDG3㈠