Talk:Pole (complex analysis)

From Wikipedia, the free encyclopedia

Mathematics Portal This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating:	Start Class	High Priority	Field: Analysis
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Nice picture, but expansion is much needed. Geometry guy 21:51, 20 May 2007 (UTC)

"A singularity which is not a pole is called an essential singularity. " This is not true... A singularity can be a removable singularity and even a branch point...

This should be changed

[edit] Examples

Some more examples of poles or various orders should be included, as well as more information relating to what a poles order means. He Who Is 19:15, 10 June 2006 (UTC)

[edit] Formal Definition

The article states: "If there exists a holomorphic function g : U → C and a nonnegative integer n such that

"

However I think g should be defined in the punctured disc around a, not necessarily in all of U. For example if f has two singularities. If this case is not being explicitly considered, then maybe it could be made more obvious? —Preceding unsigned comment added by Silasdavis (talk • contribs) 16:02, 19 November 2007 (UTC)

[edit] Hole?

How does a holomorphic function have a hole. Holomorphic functions are "defined on an open subset of the complex number plane C with values in C that are complex-differentiable at every point." Clearly, you cannot differentiate at a pole. Perhaps the author meant a non-holomorphic function?

Where do you see the word "hole" in the article? If you ask how you can have a holmorphic function defined around a hole, that's very simple, the hole is not in the domain of the function. So the domain of the function is say an open disk without its center, which is an open set. Oleg Alexandrov (talk) 02:09, 13 April 2007 (UTC)

We always talk about meromorphic functions when we talk about poles we never says "Poles of a holomorphic function" we always say "Pole of a meromorphic function". We talk about holomorphic functions as functions with no pole on their domain. By omitting the pole from the domain you may say that the function become holomorphic but studying the holomorphic functions does not include studying the poles. This is in the area of study of the behavior of meromorphic function. I think the first sentence should change to "pole of a meromorphic function" i think. ~ —Preceding unsigned comment added by Bossudenotredame (talk • contribs) 04:32, 7 February 2008 (UTC)

I have talked with my professor in Riemann Surfaces and Theta function, Dr. Marco Bertola, and he agreed that it is much more appropriate. So I'm going to change it to meromorphic functions Bossudenotredame (talk) 04:49, 12 March 2008 (UTC)