Abstract
We investigate for which real numbers α the series (4) converges, and prove that, even though it converges almost everywhere in the sense of Lebesgue to a periodic, with a period 1, odd function in L 2 ( [ 0 , 1 ] ) , it is divergent at uncountably many points, the set of which is dense in [ 0 , 1 ] . Finally, we find the Fourier expansion of the function defined by the series (4).
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