1
vote
1answer
162 views

System of quadratic complex equations

I want to solve this system of N non-linear equations without using a numerical method: $x_{k}^{2}= \alpha_{k }+ \sum\limits_{m=1}^{N} (\beta_{km} x_{m} + \psi_{km} x_{m}^{*})$ With $\left| ...
1
vote
0answers
183 views

An integral with Gamma functions (Part 2)

I was wondering if there is a generalization of the integral discussed here to a case like, \begin{equation}\int \frac{d^dq}{q^{\nu_1}\vert \vec{q} \pm \vec{k}_1\vert ^{\nu_2}\vert \vec{q} \pm ...
2
votes
0answers
194 views

Analytical continuation of electrostatic potentials

I'm having some trouble figuring out the properties with respect to analytical continuation of functions defined using an integral kernel. More particularly, I am working with the electrostatic ...
2
votes
1answer
429 views

An integral with Gamma functions

I wanted some insights about the integral in equation A.5 (page 19) in this paper, http://arxiv.org/pdf/1301.7182.pdf What is the derivation of this? Is there something more general from where this ...
4
votes
1answer
414 views

Similarity between Cauchy-Riemann eqs and Hamilton equations.

I would like to see if this idea has any applications: So CR equations are given by: $$ \frac{\partial u}{\partial x} =\frac{\partial v}{\partial y} ; \ \frac{\partial u}{\partial y}=-\frac{\partial ...
7
votes
1answer
517 views

Non-algebraic curve visualisation

Is there any software which can automatically visualise a non-algebraic complex curve, I mean the structure of it's ramification points and sheet? I think a good test example would be the Lambert ...