Morera 定理 - 香蕉空间
网页Morera 定理 • 英文 Morera’s theorem • 德文 Satz von Morera • 法文 théorème de Morera. 在复分析中, Morera 定理是判断一个函数是否全纯的条件. Cauchy 积分定理说明, 在复平面上, 全纯函数沿闭曲线的积分为 0.
莫雷拉定理 - 維基百科，自由的百科全書
网页莫雷拉定理 是一個用來判斷函數是否 全純 的定理。 如果 f 是一個 連續 的複值函數，定義在 複數平面 上的 開集 D 內，且對於所有 D 內的閉曲線 C ，都滿足. 則 f 在 D 內是全純的。 莫雷拉定理的假設等於是說 f 在 D 內具有原函數。 該定理的逆命題不一定成立。 全純函數在定義域內並不一定有 原函數 ，除非加上更多條件。 例如， 柯西積分定理 說明全純函數沿著一條 閉曲線 的 路徑積分 為零，只要函數的定義域是 單連通 的。 證明 [ 編輯] 莫雷拉定理 …
Morera's theorem - Wikiwand
网页Morera's theorem states that a continuous, complex-valued function f defined on an open set D in the complex plane that satisfies = for every closed piecewise C 1 curve in D must be holomorphic on D. The assumption of Morera's theorem is equivalent to f locally having an antiderivative on D .
Morera theorem - Encyclopedia of Mathematics
网页2014年1月12日 · A fundamental theorem in complex analysis that states that a continuous function on an open set is holomorphic if its integral over any rectifiable contour vanishes. The theorem can be generalized to several complex variables and prismatic domains.
Morera's Theorem - Vocab, Definition, and Must Know Facts
网页Morera's Theorem states that if a function is continuous on a domain and its integral over every closed contour in that domain is zero, then the function is holomorphic (complex differentiable) throughout that domain.
Morera's Theorem in complex analysis with proof (Converse of …
网页2020年8月8日 · In this video we will discuss Proof of MORERA’S THEOREM. (Converse of Cauchy’s Integral Theorem) PLAYLISTS LINK : 1. Cauchy integral formula and proof • Cauchy Integral Theorem and Formula 2...
complex analysis - Striking applications of Morera's theorem ...
网页2010年8月10日 · In Rudin's "Real and Complex Analysis" (Third Edition), Morera's Theorem assists in the proofs of the following two interesting theorems. (Here, I'm paraphrasing, not quoting.) Müntz-Szász Theorem: Let 0 <λ1 <λ2 <⋯, and let X = {1, xλ1, xλ2, …} ⊂ C[0, 1]. Then X is dense in C[0, 1] if and only if ∑ 1 λn = ∞.
Morera type theorems - Mathematics Stack Exchange
网页Morera's theorem simply states that if a function $f$ is continuous on $\Bbb{C}$ and $\int_D f(z)dz=0$ for any triangle(rectangle) $D$, then $f$ is holomorphic in $\Bbb{C}$. (the theorem is still valid if we replace $\Bbb{C}$ by a disk).
Morera's Theorem - Vocab, Definition, and Must Know Facts
网页Morera's Theorem states that if a continuous function defined on a simply connected domain has a zero integral over every closed contour in that domain, then the function is …
Morera’s theorem - PlanetMath.org
网页2018年2月9日 · Morera's theorem states that a continuous function on a region in C is analytic if its integral over any closed triangle or curve is zero. See the statement, proof and references of this theorem on PlanetMath.
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