V2EX holomorphic

Holomorphic

释义 Definition

holomorphic(全纯的):指复分析中“在某个区域内处处可复微分”的函数或性质。全纯函数在其定义域内具有很强的光滑性与结构性(例如可展开为幂级数)。(在一些语境中也会与 analytic 近似同义,但不同教材可能有细微用法差别。)

发音 Pronunciation (IPA)

/hlmrfk/

例句 Examples

A holomorphic function is complex-differentiable.
全纯函数是在复数意义下可微的函数。

If a function is holomorphic on a simply connected domain and has no zeros, then it admits a holomorphic logarithm there.
如果一个函数在单连通域上全纯且处处不为零,那么它在该区域内存在一个全纯的对数函数。

词源 Etymology

holomorphic 来自希腊语词根:**holo-**(“整体、全部”)+ -morph(“形状、形式”)+ 形容词后缀 -ic。在数学语境中可理解为“整体保持(良好)形式的”,用于描述复函数具有“处处可微、结构高度一致”的性质。

相关词 Related Words

文献与作品 Literary / Notable Works

  • Lars Ahlfors, Complex Analysis(常用复分析教材,频繁讨论 holomorphic functions)
  • John B. Conway, Functions of One Complex Variable(系统使用 “holomorphic” 术语)
  • E. M. Stein & R. Shakarchi, Complex Analysis(在复分析与傅里叶分析联系中大量出现)
  • Walter Rudin, Real and Complex Analysis(在复分析章节中使用 holomorphic/analytic 的相关概念)
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