I am not finding any document online discussing how changing the variable affects the Fourier series. Any thought on the rule ?
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Hint:
The series for $f(2x)$ is identical to the new series, so they must be the same over some interval.
To resolve this seemingly paradoxical result, ask yourself:
What's the period of the original series? What can you say about the period of the new series?
Nathaniel Bubis
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The new one has half the original period ? – Mike Harb Oct 08 '16 at 07:05