I don't know if it is the right section to post in. I have a problem with a "simple" Fourier transform. This is the function to transform: f(t)=\frac{\sin\left({2\pi t}\right)}{t}. My first idea was to write that as \sin\left({2\pi t}\right)\cdot\frac{1}{t} but then my fantasy crashed against a...
Hello everybody! I have to decompose to simple fractions the following function: V(z)=\frac{z^2-4z+4}{(z-3)(z-1)^2}. I know I can see the function as: V(z)=\frac{A}{z-3}+\frac{B}{(z-1)^2}+\frac{C}{z-1}, and that the terms A, B, C can be calculated respectively as the residues in 3 (single pole)...
Hello! I have a problem with the following exercise, in which i must calculate the ray of a power serie. This is the power serie: \sum_{K=0}^{+\infty}(k+1)z^{k+1}. I decide to use the ratio test, and so i calculate \lim_{k\rightarrow +\infty}\frac{a_{n+1}}{a_{n}} for n going to infinity and i...
Hello everybody! I'm sorry if it's not the right section to post in. I'm trying to solve this exercise:
\frac{1}{2i\pi}*\int_{8-i\infty}^{8+i\infty}\frac{e^{s(t-5)}}{(s+4)^2}ds
The request is to find the result in function of t
I know i must use the Riemann inversion formula, and so the request...