Linked Questions

3
votes
2answers
6k 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 ...
0
votes
1answer
2k 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 ...
27
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, ...
3
votes
1answer
4k views

Complex line integral

Can someone recommend an online article or introductory tutorial that will show me how to do real and complex line integrals using Mathematica?
1
vote
2answers
527 views

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: ...
7
votes
3answers
673 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. ...
6
votes
1answer
485 views

Definite Integral over a path

What does Integrate[f[z], {z, a, b, c, d}] exactly calculate? Is it $$\int_a^b f(z)\, \mathrm{d}z +\int_b^c f(z)\, \mathrm{d}z +\int_{c}^d f(z)\, \mathrm{d}z ...
0
votes
0answers
828 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 ...
5
votes
1answer
227 views

Wolfram Language 12 says this absolutely convergent series does not converge. Is there any similar example?

I am reading "Lectures on complex function theory" by Takaaki Nomura. In this book, there is the following example: $\sum_{n=1}^{\infty} \sin(\pi(2+\sqrt{3})^n)$ converges absolutely. But ...
2
votes
1answer
122 views

Integrate with complex limits

I am trying to understand how Mathematica handles the Integral with complex limits. NIntegrate[Exp[Sin[y]], {y, I, 2}] How does NIntegrate works for this limits?...
0
votes
0answers
77 views

How to calculate this integral symbolically?

How to calculate the following integral symbolically with Mathematica: $$ I = \int_0^\infty \frac{\mathrm{d}x}{(x^2+a^2)(\ln^2x+\pi^2)} $$ where $a>0$ is a real number. PS: from complex analysis,...
0
votes
0answers
74 views

How to specify this function in mathematica and take integral?

I have this function, $$F(r) = \frac{1}{r^{6}-1+i 0^{+}}$$ I don't know how to specify a function like this in Mathematica. The problem is how to specify the infinitesimal small imaginary part. ...