Tagged Questions
1
vote
0answers
44 views
Taylor series of Fourier series of triangle wave
Odd triangle wave $\text{t}(x)$ with angles at $(2x+1)\in\mathbb{Z}$ can be represented by Fourier series:
...
2
votes
1answer
149 views
Convergence of: $\sum\limits_{n=1}^{\infty} \frac{(-1)^{n+1}\sin(nx)}{n}$
Need help with checking: $\sum\limits_{n=1}^{\infty} \frac{(-1)^{n+1}\sin(nx)}{n}$
for point-wise convergence and uniform convergence of: ${-\pi} \leq x \leq {\pi}$.
0
votes
0answers
100 views
finding the fourier coefficients of $f(x) = \sum_{n=1}^{\infty} \frac{\cos(nx)}{n^2}$
This is what i know so far:
The given series uniformly converges by the M-test and that i can swap the integration and the sum when calculating the coefficients.
Apparently i am supposed to use the ...
4
votes
2answers
185 views
The relationship between Fourier coefficients of function $f$ and its continuity
How to prove that if Fourier series of function $f$ converge uniformly, then function is continuous?
5
votes
1answer
254 views
Series which are not Fourier Series
How to show that
$$
\sum_{n=2}^\infty \frac{\sin{(nx)}}{\log n}
$$
not the Fourier series of any function?
I have shown that the series is convergent by Dirichlet test.
Let $a(n)=\frac{1}{\log ...
0
votes
2answers
250 views
When convergence in mean implies uniform convergence?
With Fourier series, I'm confused about Bessel's inequality and Parseval's identity.
I understand that Bessel's inequality becomes Parseval's equality if and only if both integrals
$ ...
3
votes
0answers
117 views
Uniform convergence of a series
This problem came from the Krantz text ($2^{nd}$ ed. ch. 9, prob. 17):
Prove that the series $\displaystyle\sum_{j=1}^{\infty }{\frac{\sin{(jx)}}{j}}$ converges uniformly on compact intervals that do ...
