Tagged Questions
9
votes
4answers
291 views
Singular asymptotics of Gaussian integrals with periodic perturbations
At the bottom of page 5 of this paper by Giedrius Alkauskas it is claimed that, for a $1$-periodic continuous function $f$,
$$
\int_{-\infty}^{\infty} f(x) e^{-Ax^2}\,dx = \sqrt{\frac{\pi}{A}} ...
1
vote
0answers
28 views
Complex Fourier series of a function [duplicate]
I need to find the complex Fourier series of this function, and I'm having problems calculating these integers:
$$|a|<1$$
$$x\in [-\pi,\pi]$$
$$f(x)=\frac{1-a\cos(x)}{1-2a\cos(x)+a^2}$$
...
2
votes
2answers
232 views
Complex Fourier series
I need to find the complex Fourier series of this function, and I'm having problems calculating these integers:
$$|a|<1$$
$$x\in [-\pi,\pi]$$
$$f(x)=\frac{1-a\cos(x)}{1-2a\cos(x)+a^2}$$
...
5
votes
1answer
158 views
Tough Inverse Fourier Transform
In reference to this answer I gave the other day, I came across a very interesting function whose IFT would be nice to evaluate as part of completing the solution to the problem I answered. The ...
3
votes
2answers
94 views
Evaluate the integral $I=\int\limits_{-\infty}^{\infty} \frac{\sin^{2}u}{u^{2}}du$
To evaluate this integral I have got to use Parseval's Theorem and the fourier transform of
$$s(x)=\begin{cases}
0 & x\leq -a \\
1 & -a<x<a \\
0 & x \geq a.\end{cases}$$
This ...
2
votes
0answers
168 views
Very tricky Fourier transform
I'm trying to evaluate the following integral using complex function theory:
\begin{equation}
...
