Cauchy's residue theorem for a class of real valued functions

Title:

Cauchy's residue theorem for a class of real valued functions

Creator:

Sarić, Branko

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a0ad7dbf-6b69-4a09-817d-60c63ff937b8
uuid:a0ad7dbf-6b69-4a09-817d-60c63ff937b8

Subject:

Kurzweil-Henstock integral and Cauchy's residue theorem

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $[ a,b] $ be an interval in $\mathbb R$ and let $F$ be a real valued function defined at the endpoints of $[a,b]$ and with a certain number of discontinuities within $[ a,b] $. Assuming $F$ to be differentiable on a set $[ a,b] \backslash E$ to the derivative $f$, where $E$ is a subset of $[ a,b] $ at whose points $F$ can take values $\pm \infty $ or not be defined at all, we adopt the convention that $F$ and $f$ are equal to $0$ at all points of $E$ and show that $\mathcal {KH}\hbox {\rm -vt}\int _a^bf=F( b) -F( a) $, where $\mathcal {KH}\hbox {\rm -vt}$ denotes the total value of the {\it Kurzweil-Henstock} integral. The paper ends with a few examples that illustrate the theory.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1043-1048

Source:

Czechoslovak Mathematical Journal | 2010 Volume:60 | Number:4

Harvested from:

CDK

Metadata only:

false