Here is a few transform that I'm trying to calculate:
1. Calculate the fourier coefficient of on and thus determine the sum . I get . I'm not sure if this is correct and can't see how using any identities (e.g. Parseval) I can calculate the sum.
2. Suppose that and . Show that if is integrable then has continuous bounded derivatives.
Proceeding as in...
http://www.mathhelpforum.com/math-help/advanced-applied-math/141470-fourier-series.html
... we obtain...
(1)
... so that for is...
(2)
Now if we remember that the series (2) for converges to we obtain...
(3)
... and from (3) ...
(4)
Kind regards