Linked Questions
22 questions linked to/from How to calculate contour integrals with Mathematica?
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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_\...
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30
votes
2
answers
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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
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5
answers
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Is there an easy way of drawing a part of a circle used in a complex contour?
I see the Descarta2D package can easily draw some figures.
Unfortunately, the package is not to be found and runs on MMA 2021.
I do want to do some complex contour calculations and need some diagrams.
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- 669
28
votes
1
answer
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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, ...
- 33.5k
29
votes
3
answers
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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
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- 945
5
votes
4
answers
1k
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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 ...
- 435
9
votes
2
answers
3k
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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 ...
- 195
4
votes
2
answers
10k
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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 ...
- 71
6
votes
3
answers
550
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Integral $\int_{d_1}^{d_2} \int_{-L/2}^{L/2} \int_{-L/2}^{L/2} \frac{1}{(x^2+y^2+z^2)^3} dx dy dz$
I'm trying to calculate the following integral in Mathematica, but it seems it doesn't return an analytical closed form, neither when I give numeric values for both $d_{1,2}$ and $L$.
$$∫_{d_1}^{...
- 595
1
vote
2
answers
792
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Having problems integrating a meromorphic function [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:
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- 433
7
votes
3
answers
2k
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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,...
- 471
7
votes
3
answers
879
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.
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- 5,215
0
votes
3
answers
2k
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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 ...
- 177
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1
answer
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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 ...
- 293
4
votes
1
answer
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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 <...
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