All Questions
9 questions
6
votes
2
answers
2k
views
Why can’t mathematica find this residue?
I am trying to find the residue of the function $$f(z)=(z+1)^2e^{3/z^2}$$
at $z=0$.
I tried the following in Mathematica
Residue[(z+1)^2*Exp[3/z^2],{z,0}]
which ...
- 409
3
votes
1
answer
177
views
Generating function for residues of a complicated function
I have a rather complicated function involving 3F2 Hypergeometric functions (see below), which has infinitely many poles. I can extract the residues individually. But it would be great if I could ...
- 479
1
vote
1
answer
537
views
Laurent series 0 < |z-3| < 3
I wanna check my laurent series exercises on Mathematica, but can't seem to find a command or program to achieve the result of such type of interval.
$f(z)=\frac{1}{(z-3) z},\\1<|z-3|<3$
The ...
- 13
10
votes
1
answer
842
views
Expansion for Modified Bessel Function Around Infinity
I'm somewhat new to Mathematica, and I don't understand why I'm getting inconsistent series expansions for the modified Bessel Function of first kind near $x=\infty$.
First problem:
I get different ...
- 101
12
votes
1
answer
1k
views
Contour Integration along a contour containing two branch points
I need to compute following contour integrations:
$$f(u)=\oint_\alpha dz \sqrt{z^3+z+u} \qquad ; \qquad g(u)=\oint_\beta dz \sqrt{z^3+z+u}$$
In which $\alpha$ and $\beta$ are two contours in ...
- 221
1
vote
0
answers
312
views
A power series expansion [closed]
Consider the function, $f(z) = z\, \tanh(\pi z) \log (z^2 + a^2)$ for some $a>0$.
Now I am considering 3 different situations,
$z = i(n+0.5) - i\epsilon + \delta - it$ for $n \in \mathbb{Z}$ ...
- 1,191
30
votes
2
answers
6k
views
How does Mathematica understand branchcuts of the complex logarithm?
Say I have the function $f(x) = x \tanh(\pi x) \log (x^2 +a^2)$ where $a$ is some positive real number. Then it seems to be me that Mathematica when given such a ...
- 1,191
13
votes
2
answers
865
views
How to compute the residue of $e^{z-\frac{1}{z}}$ at z=0?
I've tried the following but it didn't work:
Residue[Exp[z - 1/z], {z, 0}]
not even this:
Residue[Exp[1/z], {z, 0}]
...
- 295
12
votes
3
answers
8k
views
Laurent series expansion
Can someone share how to find the Laurent series expansion of
$$f(z)=\frac{1}{(z^2-1)(z^2-4)}$$
centered at $0$ on the annulus $1<|z|<2$?
- 15k