List questions from branch-cuts

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Calculate the integral with branches

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Calculating the difference between $f(x+iy)$ and $f(x-iy)$ when $y\to0+$

Published on 09 Oct 2023 - 5:54

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A simple issue thats been swept under the rug.

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why including the origin in a closed path causes discontinuity in complex functions like the square root?

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Analytic continuation of incomplete beta function

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Being precise about contour integrals when dealing with branch-cuts and singularities

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Branch cuts of $\log(z^2-1)$ for unusual principal values

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Branch cut of $\log(z^2-1)$ if $\arg(z^2-1)\in\left(-\frac{7\pi}{4}, \frac{\pi}{4}\right]$

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Integrating along the closed contour crossing the branch cut

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Branch cut integral calculation by the method of residues.

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What does the argument limitation $| \arg(z)| < \frac{3\pi}{2}$ mean for the asymptotic development of $E_1(z)$?

Published on 21 Dec 2023 - 10:43

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What is meant by saying that $[f(z)]^p$ has a holomorphic branch in a neighborhood of $z_0.$

Published on 25 Dec 2023 - 11:46

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Analytically continuing a function defined via an integral

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Riemann surface of the hypergeometric function

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List Question

Double complex branch cut integration, how to?

Calculate the integral with branches

Calculating the difference between $f(x+iy)$ and $f(x-iy)$ when $y\to0+$

A simple issue thats been swept under the rug.

why including the origin in a closed path causes discontinuity in complex functions like the square root?

Analytic continuation of incomplete beta function

Being precise about contour integrals when dealing with branch-cuts and singularities

Branch cuts of $\log(z^2-1)$ for unusual principal values

Branch cut of $\log(z^2-1)$ if $\arg(z^2-1)\in\left(-\frac{7\pi}{4}, \frac{\pi}{4}\right]$

Integrating along the closed contour crossing the branch cut

Branch cut integral calculation by the method of residues.

What does the argument limitation $| \arg(z)| < \frac{3\pi}{2}$ mean for the asymptotic development of $E_1(z)$?

What is meant by saying that $[f(z)]^p$ has a holomorphic branch in a neighborhood of $z_0.$

Analytically continuing a function defined via an integral

Riemann surface of the hypergeometric function

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