4. If f : R ---+ R belongs to COO(R) and f(j) is periodic for all j...

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4. If f : R ---+ R belongs to COO(R) and f(j) is periodic for all j 2: 0, prove that Sf is term-by-term differentiable on R. In fact, show that dj f 00 dj

-d.( x) = '"' -d. (ak(f)coskx+bk(f)sinkx)

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An Introduction To Analysis

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Authors: William R. Wade

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4. If f : R ---+ R belongs to COO(R) and f(j) is periodic for all j...

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An Introduction To Analysis

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