Companal, The Complex Analysis Wiki (pre-pre-alpha)

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# New pages

- 21:19, 12 September 2008 Removable singularities theorem (hist) [483 bytes] Vipul (Talk | contribs) (New page: {{basic fact}} ==Statement== The '''removable singularities theorem''', sometimes termed the '''Riemann removable singularities theorem''', states that if <math>U</math> is a neighborhoo...)
- 20:56, 12 September 2008 Every compact Riemann surface is a branched cover of the Riemann sphere (hist) [334 bytes] Vipul (Talk | contribs) (New page: ==Statement== Let <math>S</math> be a fact about::compact Riemann surface of degree <math>g</math>. Then, <math>S</math> admits a nonconstant meromorphic function of degree at most <m...)
- 20:53, 12 September 2008 Riemann-Roch theorem (hist) [796 bytes] Vipul (Talk | contribs) (New page: ==Statement== Let <math>S</math> be a fact about::compact Riemann surface. Let <math>K</math> be a fact about::canonical divisor for <math>S</math>, and <math>D</math> be any [[fa...)
- 20:44, 12 September 2008 Uniformization theorem (hist) [733 bytes] Vipul (Talk | contribs) (New page: ==Statement== There are two components to the statement: * Any simply connected fact about::Riemann surface is conformally equivalent to one of these three: the [[fact about::open uni...)
- 20:35, 12 September 2008 Genus zero Riemann surface is conformally equivalent to Riemann sphere (hist) [2,064 bytes] Vipul (Talk | contribs) (New page: ==Statement== Any fact about::compact Riemann surface of genus zero (in other words, any compact Riemann surface that is topologically a sphere) is conformally equivalent to the [fact...)
- 18:53, 12 September 2008 Cauchy integral formula for constant functions (hist) [1,089 bytes] Vipul (Talk | contribs) (New page: ==Statement== Suppose <math>c \in \mathbb{C}</math> is a complex number, and <math>U</math> is a domain in <math>\mathbb{C}</math>. Then, if <math>D</math> is a disk centered at <math>z_0...)
- 16:22, 12 September 2008 Holomorphic function on open disk admits globally convergent power series (hist) [2,873 bytes] Vipul (Talk | contribs) (New page: ==Statement== Suppose <math>U \subseteq \mathbb{C}</math> is an open disk with center <math>z_0</math> and radius <math>R > 0</math>. Suppose <math>f: U \to \mathbb{C}</math> is a [[h...)
- 16:06, 12 September 2008 Power series is infinitely differentiable in disk of convergence (hist) [3,268 bytes] Vipul (Talk | contribs) (New page: ==Statement== Consider the fact about::power series about a point <math>z_0 \in \mathbb{C}</math> with coefficients <math>a_n \in \mathbb{C}</math>: <math>\sum a_n(z - z_0)^n</math> ...)
- 20:56, 25 May 2008 Punctured plane (hist) [201 bytes] Vipul (Talk | contribs) (New page: ==Definition== The '''punctured plane''' is the set of nonzero complex numbers, viewed as a subset of the plane. It is denoted as <math>\mathbb{C} \setminus 0</math>, or <math>\mathbb...)
- 19:56, 25 May 2008 Plane (hist) [285 bytes] Vipul (Talk | contribs) (New page: ==Definition== The '''plane''', or '''Argand plane''', or '''plane of complex numbers''', is simply the whole plane comprising complex numbers <math>\mathbb{C}</math>. This is sometimes a...)