Linked Questions

0
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0answers
62 views

Coding contour integration [duplicate]

I am struggling to understand contour integration. How would it be applied in Mathematica? I am hoping that if I see it written in Mathematica code, it will help me understand it. eg how would $$\int_\...
25
votes
2answers
4k 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 ...
28
votes
1answer
2k views

Undocumented use of Integrate: Integrating over regions

I have come across a few questions asking about integrating over regions. And while the answers are impressive there should be a better more consistent way. So my question is, are there ways, ...
28
votes
3answers
1k views

Symbolic integration error

fixed in 10.1 (windows) I'm running Mathematica 10.0.0 and encountered a disturbing error in the symbolic integration of a rather simple function ...
3
votes
4answers
1k views

How to calculate this integral?

I am trying to Integrate the following Integral : $\int_1^{\infty } \dfrac{\left(x^2-1\right)^{13/2} e^{-ax} }{x^{10}} \, dx \,\, \,\,\,\,\,\,\,\,\,\,\,\,(a=\textrm{real>0})$ Mathematica didn't ...
3
votes
2answers
3k views

How would you calculate a contour integral? [duplicate]

How would you be able to calculate a contour integral of 1/(((z-1)^2)*(z-i)) over the contour |z-1| = 1? Not sure how to type ...
5
votes
2answers
1k views

Drawing contour integral diagrams

I am $\TeX$ writing notes on complex analysis, I need to use figures of contour paths to integrate on them, how can I plot them on Mathematica, something like this adding also the $\gamma_R$ legends ...
7
votes
3answers
623 views

Different results of a definite integral $\int_0^{\cosh ^{-1}(a)} \frac{1}{\sqrt{a^2 \text{sech}^2(x)-1}}\, dx$

fixed in 10.0.2 Update I have tried like these. I think there is a bug. ...
7
votes
3answers
592 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,...
1
vote
2answers
273 views

Having problems integrating a function of a complex variable [closed]

I've tried to calculate the integral And I got the result $16i \pi ^3$. I wanted to check my calculation, so I ran this code in Mathematica: ...
0
votes
3answers
1k views

Residue theorem and multiple poles in contour integral

I had a query on multiples poles in [Contour Integral][1] using the [Residue Theorem][2]. I had an integral which I wanted to solve using the Residue Theorem. By the help of mathematica experts i ...
4
votes
1answer
613 views

How to do this complex integration on the real line?

$m, r$ are parameters in the following integral: Integrate[z Exp[I z r]/Sqrt[z^2 + m^2], {z, -∞, ∞}] How to do this integration directly? The result should be <...
0
votes
0answers
819 views

Complex integrals and residues

I have a question. I try to integrate this function: Integrate[Exp[I k z]*Exp[-Sqrt[k^2 - A^2]x]*Exp[-k^2*L^2/4]/Sqrt[k^2 - A^2], {k, -Infinity, -A}] But ...
2
votes
1answer
336 views

Numerical integration over a circle contour [duplicate]

I want to numerically integrate the following function $$f(p) = \frac{1}{2\pi i}\int_{\Gamma}\frac{1}{p}\exp\left(\frac{a^{2}}{2}\frac{1}{p}+\frac{b^{2}}{2}p\right)dp$$ where the contour $\Gamma$ ...
0
votes
1answer
658 views

Computation of complex integral over circle [duplicate]

I am beginning Mathematica user. Please show me the syntax on how to compute the following complex integral in Mathematica: $\int_{|z-2i|=10} \frac{dz}{z(1-e^{-5z})}$ What I really want is a ...

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