Linked Questions

45 votes
2 answers
23k views

How to calculate contour integrals with Mathematica?

How to calculate the integral of $\frac{1}{\sqrt{4 z^2 + 4 z + 3}}$ over the unit circle counterclockwise for each branch of the integrand?
user64494's user avatar
  • 26.3k
19 votes
3 answers
5k views

Moving the location of the branch cut in Mathematica

According to the documentation, Mathematica chooses the branch cut for $\log(z)$ to lie along the negative real axis. It it possible to change this so that it lies along the positive axis or elsewhere ...
Zzz's user avatar
  • 221
10 votes
1 answer
468 views

Using Solve to solve the equation $x^{1/3}=-1$

I am curious why this command returned no answers: Solve[x^(1/3) == -1, x] Gives this output: (* {} *) I was able to get ...
David's user avatar
  • 14.9k
7 votes
3 answers
1k views

Getting Arg[z] to go from $0$ to $2\pi$

I'm defining branch cut functions, and I'm using $\arg(z)$ as a building block. So I just spent an hour at the whiteboard assuming that $\arg(z)$ goes from $0$ to $2\pi$, and then I implement the code,...
David Roberts's user avatar
11 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 ...
QGravity's user avatar
  • 211
7 votes
1 answer
524 views

How to calculate residues using different branches of the logarithm

My goal is to be able to compute the residues of something like $z^{\alpha} R(z)$ where $0 < \alpha < 1$, $R(z)$ is rational, and the exponential can be chosen with any branch. I found a way to ...
user30420's user avatar
0 votes
3 answers
796 views

Plotting complex function

(9 Tanh[x]^8 (1 - 2 Tanh[x]^2)^2 (1 - Tanh[x]^2))/(1 + 3 I Sqrt[2/13])^2 How can I plot the function with the range of x {-10,10}?
merve's user avatar
  • 71
4 votes
1 answer
431 views

Returning all branches of a multiple-valued function

This question and answer was inspired by this closed as duplicate question. One possible definition of the n-th order root of x ...
LLlAMnYP's user avatar
  • 11.5k
0 votes
1 answer
427 views

Plotting Complex Numbers - Functions of Complex Numbers [duplicate]

So I have to generate a few different plots with z, where z is a complete number... z[x_, y_] := x + y*I F[z_] := (25*Pi*z*I)/(1 + 10*Pi*z*I) First, I need to ...
Jobelle Holcombe's user avatar
0 votes
0 answers
170 views

Is mathematica integrating $\frac{1}{x}$ correctly?

When $x<0, \quad \int \frac{1}{x}\,dx = \ln (-x) + \text{const.}$ Mathematica calculates this Assuming[x < 0, Integrate[1/x, x]] as ...
mjw's user avatar
  • 2,146
1 vote
0 answers
100 views

Defining dilogarithm with branch cut on $(-\infty,1)$

If my logarithms have a branch cut on $(0,\infty)$ then the dilogs constructed from these have a branch cut on $(-\infty,1)$. Is there a safe way to implement this in Mathematica? I tried with ...
zagaluke's user avatar
  • 111