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

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

2012-03-11

arxiv.org/abs/1203.2322v1

Czechoslovak Mathematical Journal, 2010, Volume 60, Number 4, 1043-1048

Mathematics

Classical Analysis and ODEs

6 pages

Scientific paper

10.1007/s10587-010-0068-5

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] $. Having assumed $F$ 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 $\mathcal{KH-}vt\int_{a}^{b}f=F(b) -F(a)$%, where $\mathcal{KH-}$ $vt$ denotes the total value of the \textit{% Kurzweil-Henstock} integral. The paper ends with a few examples that illustrate the theory.

Affiliated with

Also associated with

No associations

Rating

Cauchy's residue theorem for a class of real valued functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cauchy's residue theorem for a class of real valued functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cauchy's residue theorem for a class of real valued functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-14500