Consider the function f(x) = e^|x| (a) Compute its complex Fourier expansion on [, ]. (b) Find the cosine Fourier expansion of f on the

Consider the function f(x) = e^|x|

(a) Compute its complex Fourier expansion on [−π, π].

(b) Find the cosine Fourier expansion of f on the same interval.

(c) What does the series converge to, on the real line? (You can explain in words, or illustrate by a clear sketch.)