3. Let f : R R be a periodic function with period 2a. Define F(x) = f(t)dt. (a)Is F(x) always a periodic function? Under what condition is F(x) periodic? (b)Assume that f has Fourier expansion ao +E1(an cos()+b, sin(")). What is the Fourier coefficient for F(x) (assuming it is periodic)?

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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3. Let f : R → R be a periodic function with period 2a. Define F(x) = S f(t)dt.
(a)Is F(x) always a periodic function? Under what condition is F(x) periodic?
(b)Assume that ƒ has Fourier expansion ao + E1(an cos("#)+bn sin("")). What
is the Fourier coefficient for F(x) (assuming it is periodic)?
Transcribed Image Text:3. Let f : R → R be a periodic function with period 2a. Define F(x) = S f(t)dt. (a)Is F(x) always a periodic function? Under what condition is F(x) periodic? (b)Assume that ƒ has Fourier expansion ao + E1(an cos("#)+bn sin("")). What is the Fourier coefficient for F(x) (assuming it is periodic)?
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