How may one deal with a divergent Fourier series for example
$ f(x) := \sum_{n=0}^{\infty} \frac{\cos(n\theta+\alpha)}{ n^{a}}$ or
$ g(x) := \sum_{n=0}^{\infty} \frac{\sin(\log (n\theta)+\beta)}{ n^{a}} \ ? $
Do we trucante each divergent series upt to a certain number $N = N(x)$ but how to get this number $N$? Or perhaps apply Cesaro summation formula to the means $ m_{K}= \sum_{i=0}^{K}\frac{sin(i+\alpha)}{i^{\alpha}}$? However in this latter case, how do we apply the formula for the sum $ S(x) = \frac{ m_1(x)+ m_2(x)+ \cdots +m_N}{N} $ in the limit $ N \rightarrow \infty $