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_\... 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 ... 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, ... 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 ... 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 ... 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 ... 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 ... 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. ... 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,... 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: ... 3answers 1k views ### Residue theorem and multiple poles in contour integral I had a query on multiples poles in [Contour Integral] using the [Residue Theorem]. I had an integral which I wanted to solve using the Residue Theorem. By the help of mathematica experts i ... 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 <... 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 ... 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 $\Gamma$ ...
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 ...