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Question: let fx be a function on m cr by the...

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Let f(x) be a function on [-m cr by the formula Cn =- Q. I. by f(x-x. For every n E Z, define に-inf(x)dx. (I) Obtain the value of on for every n E N. (It is not necessary to consider the real part and the imagenary part separately: formal calculations as for real-valued functions will do.) (2) Show that the sum Σ creinr converges in L2(l-mn) (3) Employing the fact that the sum above converges to f(x) in the space L2 (l-π, π)), prove the equality 0o (4) Obtain the sum Σ lcil 12
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