The periodic function has a Fourier series expansion By term-by-term differentiation of this series, confirm the series

Question:

The periodic function

2 h(t) = t (-

has a Fourier series expansion

h(t) = n + 4(cost-cos 2t+cos 3t ...)

By term-by-term differentiation of this series, confirm the series obtained for f(t) in Question 24 for the case when T = π.


Data from Question 24

Show that the periodic function

f(t) = t (-T

has a Fourier series expansion

27 t f(t) = sin- -sin- +sin- T T - sin 4t T + 2t T 3t T

By term-by-term integration of this series, show that the periodic function

g(t)t (-T

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