Wikipedia:WikiProject Mathematics/PlanetMath Exchange/30-XX Functions of a complex variable

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This page provides a list of all articles available at PlanetMath in the following topic:

30-XX Functions of a complex variable.

This list will be periodically updated. Each entry in the list has three fields:

  1. PM : The first field is the link to the PlanetMath article, along with the article's object ID.
  2. WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
  3. Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
Status means PM article
N not needed
A adequately covered
C copied
M merged
NC needs copying
NM needs merging
  • Please update the WP and Status fields as appropriate.
  • if the WP field is correct please remove the qualifier "guess".
  • If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
  • If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
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[edit] 30-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

  • PM: analytic curve, id=5759 -- WP guess: analytic curve -- Status: N
I don't like this overy technical definition. I started copying it then I changed my mind. Needs a rewrite if copied. Oleg Alexandrov 10:49, 12 Feb 2005 (UTC)
See remark below at region. Oleg Alexandrov 10:49, 12 Feb 2005 (UTC)
See the comment above, about analytic arc. Oleg Alexandrov 10:49, 12 Feb 2005 (UTC)
Just a list. I doubt its use. Oleg Alexandrov (talk) 02:39, 27 November 2005 (UTC)
Our article has a more in-depth discussion and examples. Oleg Alexandrov 05:45, 11 Feb 2005 (UTC)
Note that PM defined a region to be an open and connected set. WP calls such a thing a domain, while on PM a domain is just an open set. I don't know the exact terminology (and if there is a universally agreed terminology to start with), so I will not touch this. Oleg Alexandrov 10:49, 12 Feb 2005 (UTC)
I should have said, if you have nothing better to do, go copy it over. It is a lengthy and technical definition, and it is not clear how important it really is. Never say never, but still, probably such an article has little value. Oleg Alexandrov 02:54, 12 Feb 2005 (UTC)
On PM they just have a couple of lines describing the distance in C (the absolute value of course), and that its topology is the same as of R2. Oleg Alexandrov 02:50, 12 Feb 2005 (UTC)

[edit] 30A10 Inequalities in the complex domain

Oleg Alexandrov (talk) 02:41, 27 November 2005 (UTC)

[edit] 30A99 Miscellaneous

The PM article has some info about analytic continuation on an arc, which WP does not, but WP has some other info which PM does not. Overall I like the WP article more. Oleg Alexandrov 02:58, 12 Feb 2005 (UTC)
How much can you say about an annulus anyway? Oleg Alexandrov 05:32, 13 Feb 2005 (UTC)
They are both no more than a one-liner. Certainly much more can be said about the topics. Oleg Alexandrov 04:30, 11 Feb 2005 (UTC)
The WP article needs some attention though, especially the part about path independence. Oleg Alexandrov 05:36, 13 Feb 2005 (UTC)
Techical proof of little encyclopedic value. Oleg Alexandrov 03:38, 23 Feb 2005 (UTC)
There was no such article on WP. Seeing the PM article inspired me to write on for WP. I did not just copy their article over as I did not like it. Put reference to PM in the WP article. Oleg Alexandrov 02:07, 16 Feb 2005 (UTC)
Oleg Alexandrov 04:15, 8 Feb 2005 (UTC)
The PM article is about the orientation of a curve in the complex plane, so it is quite specific to complex analysis. It is also a very short article. Will require very careful thought about where to put. Oleg Alexandrov 06:12, 17 Feb 2005 (UTC)
To big words and too many formulas for a simple fact. Oleg Alexandrov 03:38, 23 Feb 2005 (UTC)
Oleg Alexandrov (talk) 02:42, 27 November 2005 (UTC)
Oleg Alexandrov (talk) 02:42, 27 November 2005 (UTC)
Oleg Alexandrov (talk) 02:42, 27 November 2005 (UTC)
But with lots of care and by an expert. See Talk:Almost periodic function. Oleg Alexandrov 03:49, 23 Feb 2005 (UTC)
Oleg Alexandrov 01:38, 15 Feb 2005 (UTC)
It is a short theorem, I doubt it is worth its own article. Oleg Alexandrov 23:59, 14 Feb 2005 (UTC)
This is about the metric on the Riemann sphere. I don't know if it is good to put it in Riemann sphere or separateley. Oleg Alexandrov 06:05, 17 Feb 2005 (UTC)
They are both short articles. The WP one might benefit a picture. Oleg Alexandrov 20:52, 12 Feb 2005 (UTC)
On PM there is one bare-bones sentence. On WP there is a short article, but with many links to very good articles describing structures defined on the upper half-plane. Oleg Alexandrov 23:12, 10 Feb 2005 (UTC)
Well, on WP it is just less tersely explained. Would be nice to have some examples and applications. Oleg Alexandrov 23:47, 14 Feb 2005 (UTC)
Both are good articles and explain the concept well. I put a link to the PM article in the WP article. Oleg Alexandrov 23:12, 10 Feb 2005 (UTC)
A one-sentence one-formula article. Oleg Alexandrov 03:52, 23 Feb 2005 (UTC)

[edit] 30B10 Power series (including lacunary series)

Oleg Alexandrov 05:49, 11 Feb 2005 (UTC)
In the PM article they also prove that an analytic function is holomorphic, but this reverse directio is easier and not as important. Put link in the WP article to the PM article. Oleg Alexandrov 19:07, 15 Feb 2005 (UTC)
Actually the WP article is very nice. Oleg Alexandrov 05:35, 16 Feb 2005 (UTC)
Oleg Alexandrov 05:35, 16 Feb 2005 (UTC)
Oleg Alexandrov (talk) 02:43, 27 November 2005 (UTC)
Oleg Alexandrov (talk) 02:43, 27 November 2005 (UTC)
Oleg Alexandrov 05:41, 16 Feb 2005 (UTC)
Oleg Alexandrov 05:41, 16 Feb 2005 (UTC)

[edit] 30B50 Dirichlet series and other series expansions, exponential series

Oleg Alexandrov 05:16, 27 Feb 2005 (UTC)

[edit] 30B99 Miscellaneous

[edit] 30C10 Polynomials

[edit] 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral)

Oleg Alexandrov (talk) 03:49, 27 November 2005 (UTC)

[edit] 30C20 Conformal mappings of special domains

PM definition is slightly more general, in that it does not require the broken line to close to a polygon. -- Jitse Niesen 11:23, 8 Jun 2005 (UTC)

[edit] 30C35 General theory of conformal mappings

Oleg Alexandrov 05:06, 11 Feb 2005 (UTC)
It is certainly not desired to add it to the nice conformal map article we have here. Oleg Alexandrov 05:06, 11 Feb 2005 (UTC)

[edit] 30C45 Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

[edit] 30C55 General theory of univalent and multivalent functions

  • PM: Loewner chain, id=5632 -- WP guess: Loewner chain -- Status:
Oleg Alexandrov 01:25, 23 Feb 2005 (UTC)

[edit] 30C62 Quasiconformal mappings in the plane

  • PM: quasicircle, id=5604 -- WP guess: quasicircle -- Status:

[edit] 30C65 Quasiconformal mappings in $R^n$, other generalizations

[edit] 30C80 Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination

Oleg Alexandrov 03:23, 13 Feb 2005 (UTC)
Oleg Alexandrov 05:25, 27 Feb 2005 (UTC)
Oleg Alexandrov 17:55, 7 Feb 2005 (UTC)

[edit] 30C99 Miscellaneous

Oleg Alexandrov 05:09, 9 Feb 2005 (UTC)

[edit] 30D05 Functional equations in the complex domain, iteration and composition of analytic functions

[edit] 30D20 Entire functions, general theory

Put a link from the WP article to the PM article. Oleg Alexandrov 06:52, 21 Feb 2005 (UTC)
Both might need some expansion though. Oleg Alexandrov 06:52, 21 Feb 2005 (UTC)
Oleg Alexandrov 20:42, 12 Feb 2005 (UTC)
The PM article has some new things, some of which could be copied over. But that would mean rewriting the WP article, which I doubt is worth it. I instead put on the WP article a link to the PM article. Oleg Alexandrov 08:00, 9 Feb 2005 (UTC)
Oleg Alexandrov 05:26, 27 Feb 2005 (UTC)

[edit] 30D30 Meromorphic functions, general theory

Both PM and WP have short, but good enough (how much more can you say about these things?) articles on this topic, and they cover the same info. Oleg Alexandrov 08:05, 9 Feb 2005 (UTC)
linas 21:59, 13 Mar 2005 (UTC)
  • PM: general power, id=6347 -- WP guess: general power -- Status:
Oleg Alexandrov (talk) 05:03, 11 March 2006 (UTC)
Oleg Alexandrov 08:58, 17 August 2005 (UTC)
  • PM: pole, id=1200 -- WP guess: pole -- Status:
Oleg Alexandrov (talk) 05:03, 11 March 2006 (UTC)

[edit] 30D99 Miscellaneous

[edit] 30E10 Approximation in the complex domain

[edit] 30E15 Asymptotic representations in the complex domain

The WP article looks nicer overall. Oleg Alexandrov | talk 04:36, 5 Feb 2005 (UTC)

[edit] 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions

Overall, the WP article looks nicer, but the PM article has an explanation of why the name is "argument principle". One has to be very careful how these are merged (if at all). The WP article was lots of work by Dysprosia and me, and aiming for maximizing information in there but without a good thought could make the article inferior. I hope to get to this one day. Oleg Alexandrov | talk 04:41, 5 Feb 2005 (UTC)

[edit] 30E99 Miscellaneous

[edit] 30F10 Compact Riemann surfaces and uniformization

[edit] 30F15 Harmonic functions on Riemann surfaces

[edit] 30F20 Classification theory of Riemann surfaces

[edit] 30F40 Kleinian groups

[edit] 30F60 Teichmüller theory

[edit] 30F99 Miscellaneous

[edit] 30H05 Spaces and algebras of analytic functions

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