Let suppose to have the periodic function defined in as...
(1)
... so that it can be written in Fourier series as...
(2)
The can be computed in the usual way...
(3)
Now we combine the results and obtain ...
(4)
Kind regards
I don't think it telescopes to any simple value or a familiar series...
On the right track, though. I did exactly the same up to this step:
I think what you've found is the sum of the series , not
EDIT: I'm wondering whether can be found in the same way? It would be nice!