Theorem of the convergence of the series of fourier!
5080
How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?
22109
Convergence of $\int_0^\infty \sin(t)/t^\gamma \mathrm{d}t$
100473
Prove convergence of series
87389
convergence of the series $\sum u_n, u_n = \frac{n^n x^n}{n!}$ for $x>0$
148940
$\sum_{n=1}^\infty\frac1{n^6}=\frac{\pi^6}{945}$ by Fourier series of $x^2$
5167
Finding the limit that involves Fourier coefficients,
67006
Sequence of functions: Convergence
4956
Connection between Fourier transform and Taylor series
56867
Convergence proof that involves integral
48763
Convergence of $\sum_{n=1}^\infty \frac{\cos(n)}{n}$
150000
Convergence of the sequence $\frac{1}{n\sin(n)}$
119133
there is $M<\infty$ such that $\sum_{n} |\hat{f}(n)|\le M\int_{0}^{2\pi}|f(t)|dt$ for each $f\in X$
154311
Proving convergence of a series and then finding limit
84181
Is there a cleaner proof of convergence for this almost-telescoping series
129849
Convergence of the series $\sum_{n=1}^{\infty}\frac{e^n\,n!}{n^n}$
7727
Convergence of series $\sum_{n=1}^\infty\sin(n)\cdot\sin(1/n)$
149895
A more convenient Fourier series