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(Hint: We know that that is, the Fourier series of such a function f is converge

ID: 2945528 • Letter: #

Question

(Hint: We know that

that is, the Fourier series of such a function f is convergent for every x. To see the uniformconvergence, by applying integration by parts twice to the above integral expressions for an, bn, youwill be able to see how fast the coecients an, bn converges to 0. This will help you to prove theuniform convergence of the Fourier series. Keep in mind that f is a twice continuously dierentiableperiodic function, which means that f, f, fare uniformly continuous and uniformly bounded.)

Explanation / Answer

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