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

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)


 * PM: domain, id=669 -- WP guess: domain -- Status:
 * See remark below at region. Oleg Alexandrov 10:49, 12 Feb 2005 (UTC)


 * PM: extended boundary, id=5635 -- WP guess: extended boundary -- Status:


 * PM: free analytic boundary arc, id=5758 -- WP guess: free analytic boundary arc -- Status: N
 * See the comment above, about analytic arc. Oleg Alexandrov 10:49, 12 Feb 2005 (UTC)


 * PM: fundamental theorems in complex analysis, id=6656 -- WP guess: fundamental theorems in complex analysis -- Status: N
 * Just a list. I doubt its use. Oleg Alexandrov (talk) 02:39, 27 November 2005 (UTC)


 * PM: isolated singularity, id=4939 -- WP: isolated singularity -- Status: A
 * Our article has a more in-depth discussion and examples. Oleg Alexandrov 05:45, 11 Feb 2005 (UTC)


 * PM: region, id=670 -- WP guess: region -- Status:
 * 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)


 * PM: simple boundary point, id=5885 -- WP guess: simple boundary point -- Status: N
 * 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)


 * PM: topology of the complex plane, id=4295 -- WP: complex number -- Status: A
 * 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)

30A10 Inequalities in the complex domain

 * PM: Hadamard three-circle theorem, id=5605 -- WP: Hadamard three-circle theorem -- Status: C
 * Oleg Alexandrov (talk) 02:41, 27 November 2005 (UTC)


 * PM: proof of Hadamard three-circle theorem, id=7943new! -- WP guess: proof of Hadamard three-circle theorem -- Status:

30A99 Miscellaneous

 * PM: analytic continuation, id=6287 -- WP: analytic continuation -- Status: A
 * 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)


 * PM: annulus, id=4202 -- WP: annulus -- Status: A
 * How much can you say about an annulus anyway? Oleg Alexandrov 05:32, 13 Feb 2005 (UTC)


 * PM: conformally equivalent, id=3729 -- WP: conformally equivalent -- Status: A
 * 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)


 * PM: contour integral, id=3198 -- WP: contour integral -- Status: A
 * The WP article needs some attention though, especially the part about path independence. Oleg Alexandrov 05:36, 13 Feb 2005 (UTC)


 * PM: limit for exp(z), id=6144 -- WP guess: Exponential function -- Status: N
 * Techical proof of little encyclopedic value. Oleg Alexandrov 03:38, 23 Feb 2005 (UTC)


 * PM: locally bounded, id=5752 -- WP: locally bounded -- Status: A
 * 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)


 * PM: normal family, id=5753 -- WP: normal family -- Status: C
 * Oleg Alexandrov 04:15, 8 Feb 2005 (UTC)


 * PM: orientation, id=3292 -- WP: orientation (complex analysis), orientation (mathematics), orientability -- Status: NC
 * 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)


 * PM: persistence of analytic relations, id=6373 -- WP guess: analytic function -- Status: N
 * To big words and too many formulas for a simple fact. Oleg Alexandrov 03:38, 23 Feb 2005 (UTC)


 * PM: proof of Riemann mapping theorem, id=6151 -- WP guess: proof of Riemann mapping theorem -- Status: N
 * Oleg Alexandrov (talk) 02:42, 27 November 2005 (UTC)


 * PM: proof of rigidity theorem for analytic functions, id=6282 -- WP guess: proof of rigidity theorem for analytic functions -- Status: N
 * Oleg Alexandrov (talk) 02:42, 27 November 2005 (UTC)


 * PM: proof of Weierstrass M-test, id=3336 -- WP guess: proof of Weierstrass M-test -- Status: N
 * Oleg Alexandrov (talk) 02:42, 27 November 2005 (UTC)


 * PM: quasiperiodic function, id=6280 -- WP: quasiperiodic function, Almost periodic function -- Status: NM
 * But with lots of care and by an expert. See Talk:Almost periodic function. Oleg Alexandrov 03:49, 23 Feb 2005 (UTC)


 * PM: Riemann mapping theorem, id=3728 -- WP: Riemann mapping theorem -- Status: A
 * Oleg Alexandrov 01:38, 15 Feb 2005 (UTC)


 * PM: rigidity theorem for analytic functions, id=6281 -- WP : analytic function, Proof that holomorphic functions are analytic -- Status: A
 * It is a short theorem, I doubt it is worth its own article. Oleg Alexandrov 23:59, 14 Feb 2005 (UTC)


 * PM: spherical metric, id=5775 -- WP: spherical metric -- Status: NC
 * 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)


 * PM: unit disk, id=4277 -- WP: unit disk -- Status: A
 * They are both short articles. The WP one might benefit a picture. Oleg Alexandrov 20:52, 12 Feb 2005 (UTC)


 * PM: upper half-plane, id=4278 -- WP: upper half-plane -- Status: A
 * 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)


 * PM: Weierstrass M-test, id=3293 -- WP: Weierstrass M-test -- Status: A
 * 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)


 * PM: Weierstrass' theorem on addition formulas, id=6406 -- WP guess: Weierstrass' theorem on addition formulas -- Status:


 * PM: winding number, id=3291 -- WP: winding number -- Status: A
 * 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)


 * PM: winding number and fundamental group, id=3340 -- WP guess: winding number and fundamental group -- Status: N
 * A one-sentence one-formula article. Oleg Alexandrov 03:52, 23 Feb 2005 (UTC)


 * PM: z_0 is a pole of f, id=4919 -- WP guess: z_0 is a pole of f -- Status:


 * PM: estimating theorem of contour integral, id=7138 -- WP guess: estimating theorem of contour integral -- Status:


 * PM: proof of equivalence of formulas for exp, id=7210 -- WP guess: proof of equivalence of formulas for exp -- Status:


 * PM: sine integral, id=6844 -- WP guess: sine integral -- Status:


 * PM: sine integral at infinity, id=7082 -- WP guess: sine integral at infinity -- Status:


 * PM: analytic continuation by power series, id=7632new! -- WP guess: analytic continuation by power series -- Status:


 * PM: analytic continuation of Riemann zeta (using integral), id=9157new! -- WP guess: analytic continuation of Riemann zeta (using integral) -- Status:


 * PM: complex tangent and cotangent, id=9074new! -- WP guess: complex tangent and cotangent -- Status:


 * PM: example of analytic continuation, id=9118new! -- WP guess: example of analytic continuation -- Status:


 * PM: Green functions and conformal mapping, id=7963new! -- WP guess: Green functions and conformal mapping -- Status:


 * PM: identity theorem of holomorphic functions, id=9016new! -- WP guess: identity theorem of holomorphic functions -- Status:


 * PM: monodromy group, id=8501new! -- WP guess: monodromy group -- Status:


 * PM: natural boundary, id=9065new! -- WP guess: natural boundary -- Status:


 * PM: periodic functions, id=9106new! -- WP guess: periodic functions -- Status:


 * PM: persistence of differential equations, id=8475new! -- WP guess: persistence of differential equations -- Status:


 * PM: proof of estimating theorem of contour integral, id=7723new! -- WP guess: proof of estimating theorem of contour integral -- Status:


 * PM: proof of open mapping theorem, id=8537new! -- WP guess: proof of open mapping theorem -- Status:


 * PM: topic entry on complex analysis, id=9009new! -- WP guess: topic entry on complex analysis -- Status:


 * PM: topic entry on series of complex terms, id=9851new! -- WP guess: topic entry on series of complex terms -- Status:


 * PM: Weierstrass M-test for continuous functions, id=8225new! -- WP guess: Weierstrass M-test for continuous functions -- Status:


 * PM: zeros and poles of rational function, id=9084new! -- WP guess: zeros and poles of rational function -- Status:

30B10 Power series (including lacunary series)

 * PM: Euler relation, id=714 -- WP: Euler's formula -- Status: A
 * Oleg Alexandrov 05:49, 11 Feb 2005 (UTC)


 * PM: existence of power series, id=3298 -- WP: Proof that holomorphic functions are analytic -- Status: A
 * 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)


 * PM: Laurent series, id=1152 -- WP: Laurent series -- Status: A
 * Actually the WP article is very nice. Oleg Alexandrov 05:35, 16 Feb 2005 (UTC)


 * PM: power series, id=2793 -- WP: power series -- Status: A
 * Oleg Alexandrov 05:35, 16 Feb 2005 (UTC)


 * PM: proof of radius of convergence, id=3890 -- WP guess: proof of radius of convergence -- Status: N
 * Oleg Alexandrov (talk) 02:43, 27 November 2005 (UTC)


 * PM: proof of radius of convergence of a complex function, id=6279 -- WP guess: proof of radius of convergence of a complex function -- Status: N
 * Oleg Alexandrov (talk) 02:43, 27 November 2005 (UTC)


 * PM: radius of convergence, id=2794 -- WP: radius of convergence -- Status: A
 * Oleg Alexandrov 05:41, 16 Feb 2005 (UTC)


 * PM: radius of convergence of a complex function, id=6278 -- WP: radius of convergence -- Status: A
 * Oleg Alexandrov 05:41, 16 Feb 2005 (UTC)


 * PM: coefficients of Laurent series, id=7130 -- WP guess: coefficients of Laurent series -- Status:


 * PM: series inversion, id=7585 -- WP guess: series inversion -- Status:


 * PM: identity theorem of power series, id=9017new! -- WP guess: identity theorem of power series -- Status:


 * PM: indirect proof of identity theorem of power series, id=9030new! -- WP guess: indirect proof of identity theorem of power series -- Status:


 * PM: proof of identity theorem of power series, id=9027new! -- WP guess: proof of identity theorem of power series -- Status:


 * PM: proof of identity theorem of power series, id=9047new! -- WP guess: proof of identity theorem of power series -- Status:


 * PM: Weierstrass double series theorem, id=9038new! -- WP guess: Weierstrass double series theorem -- Status:

30B40 Analytic continuation

 * PM: analytic continuation of gamma function, id=9342new! -- WP guess: analytic continuation of gamma function -- Status:

30B50 Dirichlet series and other series expansions, exponential series

 * PM: Dirichlet series, id=4764 -- WP: Dirichlet series -- Status: A
 * Oleg Alexandrov 05:16, 27 Feb 2005 (UTC)

30B99 Miscellaneous

 * PM: theorems on complex function series, id=9032new! -- WP guess: theorems on complex function series -- Status:

30C10 Polynomials

 * PM: polynomially convex hull, id=5833 -- WP guess: polynomially convex hull -- Status:

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

 * PM: Hurwitz's theorem, id=5756 -- WP: Hurwitz's theorem -- Status: C
 * Oleg Alexandrov (talk) 03:49, 27 November 2005 (UTC)


 * PM: Mason-Stothers theorem, id=4554 -- WP guess: Mason-Stothers theorem -- Status:


 * PM: Weierstrass factorization theorem, id=5794 -- WP guess: Weierstrass factorization theorem -- Status:


 * PM: zeroes of analytic functions are isolated, id=4285 -- WP guess: zeroes of analytic functions are isolated -- Status:

30C20 Conformal mappings of special domains

 * PM: automorphisms of unit disk, id=4245 -- WP guess: automorphisms of unit disk -- Status:


 * PM: Schwarz-Christoffel transformation, id=6289 -- WP: Schwarz-Christoffel mapping -- Status: A
 * 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)


 * PM: unit disk upper half-plane conformal equivalence theorem, id=4279 -- WP guess: unit disk upper half-plane conformal equivalence theorem -- Status:


 * PM: cross ratio, id=7223 -- WP guess: cross ratio -- Status:


 * PM: Schwarz-Christoffel transformation (circular version), id=9136new! -- WP guess: Schwarz-Christoffel transformation (circular version) -- Status:

30C35 General theory of conformal mappings

 * PM: conformal mapping theorem, id=4220 -- WP: conformal map -- Status: A
 * Oleg Alexandrov 05:06, 11 Feb 2005 (UTC)


 * PM: proof of conformal mapping theorem, id=4502 -- WP guess: proof of conformal mapping theorem -- Status: N
 * 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)


 * PM: Schwarz reflection principle, id=5757 -- WP guess: Schwarz reflection principle -- Status:

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

 * PM: Bieberbach's conjecture, id=5899 -- WP guess: Bieberbach's conjecture -- Status:


 * PM: Blaschke product, id=5795 -- WP guess: Blaschke product -- Status:


 * PM: Koebe 1/4 theorem, id=5896 -- WP guess: Koebe 1/4 theorem -- Status:


 * PM: Koebe distortion theorem, id=5886 -- WP guess: Koebe distortion theorem -- Status:


 * PM: Koebe function, id=5888 -- WP guess: Koebe function -- Status:


 * PM: schlicht functions, id=5890 -- WP guess: schlicht functions -- Status:

30C55 General theory of univalent and multivalent functions

 * PM: conformal radius, id=5771 -- WP guess: conformal radius -- Status:


 * PM: Loewner chain, id=5632 -- WP guess: Loewner chain -- Status:


 * PM: univalent analytic function, id=5633 -- WP: univalent analytic function -- Status: C
 * Oleg Alexandrov 01:25, 23 Feb 2005 (UTC)

30C62 Quasiconformal mappings in the plane

 * PM: Beltrami differential equation, id=5557 -- WP guess: Beltrami differential equation -- Status:


 * PM: Beurling-Ahlfors quasiconformal extension, id=5517 -- WP guess: Beurling-Ahlfors quasiconformal extension -- Status:


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


 * PM: quasiconformal mapping, id=5515 -- WP guess: quasiconformal mapping -- Status:

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

 * PM: Hardy's theorem, id=5798 -- WP: Hardy's theorem -- Status: C
 * Oleg Alexandrov 03:23, 13 Feb 2005 (UTC)


 * PM: maximum principle, id=3078 -- WP: maximum principle -- Status: A
 * Oleg Alexandrov 05:25, 27 Feb 2005 (UTC)


 * PM: Phragmén-Lindelöf theorem, id=5634 -- WP guess: Phragmén-Lindelöf principle -- Status:


 * PM: proof of Schwarz lemma, id=3057 -- WP guess: proof of Schwarz lemma -- Status:


 * PM: proof of weak maximum principle for real domains, id=6152 -- WP guess: proof of weak maximum principle for real domains -- Status:


 * PM: Schwarz lemma, id=3047 -- WP: Schwarz lemma -- Status: C
 * Oleg Alexandrov 17:55, 7 Feb 2005 (UTC)


 * PM: proof of maximal modulus principle, id=7728new! -- WP guess: proof of maximal modulus principle -- Status:

30C99 Miscellaneous

 * PM: Montel's theorem, id=5754 -- WP: Montel's theorem -- Status: C
 * Oleg Alexandrov 05:09, 9 Feb 2005 (UTC)

30D10 Representations of entire functions by series and integrals

 * PM: Harnack theorem, id=8099new! -- WP guess: Harnack theorem -- Status:


 * PM: Plemelj formulas, id=8079new! -- WP guess: Plemelj formulas -- Status:


 * PM: Schwarz and Poisson formulas, id=8163new! -- WP guess: Schwarz and Poisson formulas -- Status:

30D20 Entire functions, general theory

 * PM: complex exponential function, id=6341 -- WP: exponential function -- Status: A
 * Put a link from the WP article to the PM article. Oleg Alexandrov 06:52, 21 Feb 2005 (UTC)


 * PM: complex logarithm, id=6342 -- WP guess: complex logarithm -- Status:


 * PM: entire function, id=1148 -- WP: entire function -- Status: A
 * Both might need some expansion though. Oleg Alexandrov 06:52, 21 Feb 2005 (UTC)


 * PM: holomorphic, id=1146 -- WP: holomorphic function -- Status: A
 * Oleg Alexandrov 20:42, 12 Feb 2005 (UTC)


 * PM: Liouville's theorem, id=1145 -- WP: Liouville's theorem (complex analysis) -- Status: A
 * 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)


 * PM: Morera's theorem, id=3339 -- WP: Morera's theorem -- Status: A
 * Oleg Alexandrov 05:26, 27 Feb 2005 (UTC)


 * PM: proof of Liouville's theorem, id=3254 -- WP guess: proof of Liouville's theorem -- Status:


 * PM: properties of entire functions, id=6545 -- WP guess: properties of entire functions -- Status:


 * PM: space of analytic functions, id=5918 -- WP guess: space of analytic functions -- Status:


 * PM: periodicity of exponential function, id=7107 -- WP guess: periodicity of exponential function -- Status:


 * PM: proof of addition formula of exp, id=8715new! -- WP guess: proof of addition formula of exp -- Status:


 * PM: proof of extended Liouville's theorem, id=8431new! -- WP guess: proof of extended Liouville's theorem -- Status:

30D30 Meromorphic functions, general theory

 * PM: Casorati-Weierstrass theorem, id=4143 -- WP guess: Casorati-Weierstrass theorem -- Status:


 * PM: essential singularity, id=4132 -- WP: essential singularity -- Status: A
 * 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)


 * PM: gamma function, id=955 -- WP: gamma function -- Status: A
 * linas 21:59, 13 Mar 2005 (UTC)


 * PM: general power, id=6347 -- WP guess: general power -- Status:


 * PM: Marty's theorem, id=5774 -- WP guess: Marty's theorem -- Status:


 * PM: meromorphic, id=1199 -- WP: meromorphic function -- Status: A
 * Oleg Alexandrov (talk) 05:03, 11 March 2006 (UTC)


 * PM: Mittag-Leffler's theorem, id=3732 -- WP: Mittag-Leffler's theorem -- Status: A
 * Oleg Alexandrov 08:58, 17 August 2005 (UTC)


 * PM: multiplication formula for gamma function, id=6368 -- WP guess: multiplication formula for gamma function -- Status:


 * PM: pole, id=1200 -- WP guess: pole -- Status:


 * PM: proof of Casorati-Weierstrass theorem, id=4144 -- WP guess: proof of Casorati-Weierstrass theorem -- Status:


 * PM: proof of multiplication formula for gamma function, id=6369 -- WP guess: proof of multiplication formula for gamma function -- Status:


 * PM: proof of Riemann's removable singularity theorem, id=4153 -- WP guess: proof of Riemann's removable singularity theorem -- Status:


 * PM: residue, id=1153 -- WP guess: residue (complex analysis) -- Status: A
 * Oleg Alexandrov (talk) 05:03, 11 March 2006 (UTC)


 * PM: Riemann's removable singularity theorem, id=4152 -- WP guess: Riemann's removable singularity theorem -- Status:


 * PM: simple pole, id=3746 -- WP guess: simple pole -- Status:


 * PM: spherical derivative, id=5773 -- WP guess: spherical derivative -- Status:


 * PM: incomplete gamma function, id=7536 -- WP guess: incomplete gamma function -- Status:


 * PM: incomplete gamma function recurrence formula, id=7537 -- WP guess: incomplete gamma function recurrence formula -- Status:


 * PM: Riemann's removable singularity theorem in several variables, id=7492 -- WP guess: Riemann's removable singularity theorem in several variables -- Status:


 * PM: digamma and polygamma function, id=7890new! -- WP guess: digamma and polygamma function -- Status:


 * PM: Euler reflection formula, id=8539new! -- WP guess: Euler reflection formula -- Status:


 * PM: evaluating the gamma function at 1/2, id=9223new! -- WP guess: evaluating the gamma function at 1/2 -- Status:


 * PM: Gauss' digamma theorem, id=8542new! -- WP guess: Gauss' digamma theorem -- Status:


 * PM: Hankel contour integral, id=9847new! -- WP guess: Hankel contour integral -- Status:


 * PM: meromorphic extension, id=8193new! -- WP guess: meromorphic extension -- Status:


 * PM: partial fraction series for digamma function, id=8540new! -- WP guess: partial fraction series for digamma function -- Status:


 * PM: proof of Gauss' digamma theorem, id=8550new! -- WP guess: proof of Gauss' digamma theorem -- Status:


 * PM: table of partial fraction expansions, id=7692new! -- WP guess: table of partial fraction expansions -- Status:


 * PM: technique for computing residues, id=8467new! -- WP guess: technique for computing residues -- Status:

30D99 Miscellaneous

 * PM: Möbius transformation, id=2181 -- WP guess: Möbius transformation -- Status:

30E10 Approximation in the complex domain

 * PM: Mergelyan's theorem, id=5897 -- WP guess: Mergelyan's theorem -- Status:


 * PM: Runge's theorem, id=3731 -- WP guess: Runge's theorem -- Status:

30E15 Asymptotic representations in the complex domain

 * PM: Stirling's approximation, id=953 -- WP guess: Stirling's approximation -- Status: A
 * The WP article looks nicer overall. Oleg Alexandrov | talk 04:36, 5 Feb 2005 (UTC)


 * PM: weaker version of Stirling's approximation, id=8573new! -- WP guess: weaker version of Stirling's approximation -- Status:

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

 * PM: absolute convergence implies convergence for an infinite product, id=4227 -- WP guess: absolute convergence implies convergence for an infinite product -- Status:


 * PM: absolute convergence of infinite product, id=4226 -- WP guess: absolute convergence of infinite product -- Status:


 * PM: argument principle, id=6133 -- WP guess: argument principle -- Status: NM
 * 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)


 * PM: Cauchy integral formula, id=1150 -- WP guess: Cauchy integral formula -- Status:


 * PM: Cauchy integral theorem, id=3253 -- WP guess: Cauchy integral theorem -- Status:


 * PM: Cauchy residue theorem, id=1154 -- WP guess: Cauchy residue theorem -- Status:


 * PM: closed curve theorem, id=1149 -- WP guess: closed curve theorem -- Status:


 * PM: conformal mapping, id=4219 -- WP guess: conformal mapping -- Status:


 * PM: conformal Möbius circle map theorem, id=4223 -- WP guess: conformal Möbius circle map theorem -- Status:


 * PM: convergence condition of infinite product, id=6202 -- WP guess: convergence condition of infinite product -- Status:


 * PM: convergence criterion for infinite product, id=6503 -- WP guess: convergence criterion for infinite product -- Status:


 * PM: convergence/divergence for an infinite product, id=4230 -- WP guess: convergence/divergence for an infinite product -- Status:


 * PM: example of conformal mapping, id=4241 -- WP guess: example of conformal mapping -- Status:


 * PM: examples of infinite products, id=5391 -- WP guess: examples of infinite products -- Status:


 * PM: Gauss' mean value theorem, id=4216 -- WP guess: Gauss' mean value theorem -- Status:


 * PM: link between infinite products and sums, id=4368 -- WP guess: link between infinite products and sums -- Status:


 * PM: Möbius circle transformation theorem, id=4221 -- WP guess: Möbius circle transformation theorem -- Status:


 * PM: Möbius transformation cross-ratio preservation theorem, id=4222 -- WP guess: Möbius transformation cross-ratio preservation theorem -- Status:


 * PM: order of factors in infinite product, id=6204 -- WP guess: order of factors in infinite product -- Status:


 * PM: proof of absolute convergence implies convergence for an infinite product, id=4371 -- WP guess: proof of absolute convergence implies convergence for an infinite product -- Status:


 * PM: proof of argument principle, id=6134 -- WP guess: proof of argument principle -- Status:


 * PM: proof of Cauchy integral formula, id=3105 -- WP guess: proof of Cauchy integral formula -- Status:


 * PM: proof of Cauchy residue theorem, id=4377 -- WP guess: proof of Cauchy residue theorem -- Status:


 * PM: proof of closed curve theorem, id=4164 -- WP guess: proof of closed curve theorem -- Status:


 * PM: proof of conformal Möbius circle map theorem, id=4244 -- WP guess: proof of conformal Möbius circle map theorem -- Status:


 * PM: proof of Gauss' mean value theorem, id=4217 -- WP guess: proof of Gauss' mean value theorem -- Status:


 * PM: proof of Goursat's theorem, id=3261 -- WP guess: proof of Goursat's theorem -- Status:


 * PM: proof of Möbius circle transformation theorem, id=4282 -- WP guess: proof of Möbius circle transformation theorem -- Status:


 * PM: Proof of Möbius transformation cross-ratio preservation theorem, id=5553 -- WP guess: Proof of Möbius transformation cross-ratio preservation theorem -- Status:


 * PM: proof of Rouché's theorem, id=6132 -- WP guess: proof of Rouché's theorem -- Status:


 * PM: proof of Simultaneous converging or diverging of product and sum theorem, id=4225 -- WP guess: proof of Simultaneous converging or diverging of product and sum theorem -- Status:


 * PM: Rouché's theorem, id=4218 -- WP guess: Rouché's theorem -- Status:


 * PM: simultaneous converging or diverging of product and sum theorem, id=4224 -- WP guess: simultaneous converging or diverging of product and sum theorem -- Status:


 * PM: example of using residue theorem, id=7136 -- WP guess: example of using residue theorem -- Status:


 * PM: proof of convergence criterion for infinite product, id=7506 -- WP guess: proof of convergence criterion for infinite product -- Status:


 * PM: second form of Cauchy integral theorem, id=7139 -- WP guess: second form of Cauchy integral theorem -- Status:


 * PM: inversion of plane, id=9542new! -- WP guess: inversion of plane -- Status:


 * PM: proof of convergence condition of infinite product, id=9738new! -- WP guess: proof of convergence condition of infinite product -- Status:


 * PM: proof of converse of Möbius transformation cross-ratio preservation theorem, id=9316new! -- WP guess: proof of converse of Möbius transformation cross-ratio preservation theorem -- Status:


 * PM: proof of criterion for conformal mapping of Riemannian spaces, id=8505new! -- WP guess: proof of criterion for conformal mapping of Riemannian spaces -- Status:


 * PM: simple example of composed conformal mapping, id=9023new! -- WP guess: simple example of composed conformal mapping -- Status:


 * PM: zero as contour integral, id=9008new! -- WP guess: zero as contour integral -- Status:

30E99 Miscellaneous

 * PM: Cauchy-Riemann equations, id=3281 -- WP guess: Cauchy-Riemann equations -- Status:


 * PM: Cauchy-Riemann equations (complex coordinates), id=5909 -- WP guess: Cauchy-Riemann equations (complex coordinates) -- Status:


 * PM: Cauchy-Riemann equations (polar coordinates), id=5423 -- WP guess: Cauchy-Riemann equations (polar coordinates) -- Status:


 * PM: proof of the Cauchy-Riemann equations, id=3282 -- WP guess: proof of the Cauchy-Riemann equations -- Status:


 * PM: proof to Cauchy-Riemann equations (polar coordinates), id=5504 -- WP guess: proof to Cauchy-Riemann equations (polar coordinates) -- Status:


 * PM: removable singularity, id=3289 -- WP guess: removable singularity -- Status:


 * PM: \bar{\partial} operator, id=6931 -- WP guess: \bar\partial operator -- Status:


 * PM: Paley-Wiener theorem, id=7275 -- WP guess: Paley-Wiener theorem -- Status:


 * PM: identity theorem, id=9491new! -- WP guess: identity theorem -- Status:

30F10 Compact Riemann surfaces and uniformization

 * PM: proof of the uniformization theorem, id=7558 -- WP guess: proof of the uniformization theorem -- Status:


 * PM: uniformization theorem, id=7556 -- WP guess: uniformization theorem -- Status:

30F15 Harmonic functions on Riemann surfaces

 * PM: a harmonic function on a graph which is bounded below and nonconstant, id=3042 -- WP guess: a harmonic function on a graph which is bounded below and nonconstant -- Status:


 * PM: example of harmonic functions on graphs, id=3073 -- WP guess: example of harmonic functions on graphs -- Status:


 * PM: Gauss' mean value theorem for harmonic functions, id=6658 -- WP guess: Gauss' mean value theorem for harmonic functions -- Status:


 * PM: harmonic conjugate function, id=6392 -- WP: harmonic conjugate function -- Status: A
 * Oleg Alexandrov (talk) 01:42, 8 April 2007 (UTC)


 * PM: harmonic function, id=3029 -- WP: harmonic function -- Status: A
 * Oleg Alexandrov (talk) 01:42, 8 April 2007 (UTC)


 * PM: Harnack's principle, id=6657 -- WP: Harnack's principle -- Status: C
 * Oleg Alexandrov (talk) 02:18, 26 March 2007 (UTC)

30F60 Teichmüller theory

 * PM: Teichmüller space, id=5799 -- WP guess: Teichmüller space -- Status:

30F99 Miscellaneous

 * PM: construction of Riemann surface using paths, id=6376 -- WP guess: construction of Riemann surface using paths -- Status:


 * PM: monodromy theorem, id=6380 -- WP: monodromy theorem -- Status: A
 * Oleg Alexandrov (talk) 02:15, 9 April 2007 (UTC)


 * PM: Riemann surface, id=6297 -- WP guess: Riemann surface -- Status:

30H05 Spaces and algebras of analytic functions

 * PM: factorization theorem for H^\infty functions, id=7523 -- WP guess: factorization theorem for H^\infty functions -- Status:


 * PM: inner function, id=7522 -- WP guess: inner function -- Status: