- #1
binbagsss
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Homework Statement
I have ## f(t) = \sum\limits^{\infty}_0 a_{n} e^{2 \pi i n t} ## [1]
and ## g(t) = \sum\limits^{\infty}_0 b_{n} e^{ \pi i n t} ## [2]
I want to show that ##b_n = a _{2n} ##
Homework Equations
see above.
The Attempt at a Solution
[/B]
So obviously you want to use the orthogonality to obtain the Fourier coeffients, integrating the LHS multiplied by the negative exponential over the period. Period in [1] is ##2\pi## and the period in [2] is ##\pi ##.
So I have:
from [1]: ##\int^{2 \pi } _{0} f(t) e^{- 2 \pi i n t} dt= a_{n} ##
and
from [2]: ##\int^{\pi } _{0} g(t) e^{- \pi i n t} dt = b_{n} ##
I'm unsure what to do next,
Many thanks in advance.
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