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May 27, 2021 at 11:18 comment added Jochen Wengenroth Yes, indeed. This is another reason that the particular $f$ can't be an example.
May 27, 2021 at 10:32 comment added Bazin Thanks for your example: you are certainly right that oscillatory behaviour should be the key of this question, but I guess that for your function the series of $c_n$ is absolutely convergent (as $e^{-n}$).
May 27, 2021 at 5:16 history answered Jochen Wengenroth CC BY-SA 4.0