V2EX analytic function

Analytic Function

定义 Definition

解析函数(解析的函数):在某个区域内可以用收敛的幂级数表示的函数。
在复分析中,通常指在区域内处处复可微(全纯, holomorphic)的函数;在实变量情境中也可指实解析函数

发音 Pronunciation

/nltk fkn/

例句 Examples

An analytic function can be expanded as a power series near a point.
解析函数在某点附近可以展开为幂级数。

In complex analysis, every analytic function on a simply connected domain has an antiderivative, which leads to powerful integral theorems.
在复分析中,定义在单连通区域上的解析函数都存在原函数,这会导出一些非常有力的积分定理。

词源 Etymology

analytic 来自希腊语 analytikos(“分解的、分析的”),与 analysis(分析)同源;function 源自拉丁语 functio(“执行、作用”)。合在一起,analytic function 强调这类函数具有“可被分析/展开”的结构特征(例如可用幂级数表示)。

相关词 Related Words

文学与经典作品 Literary Works

  • Complex Analysis(Lars Ahlfors)
  • Complex Analysis(Elias M. Stein & Rami Shakarchi)
  • Functions of One Complex Variable I(John B. Conway)
  • Theory of Functions(E. C. Titchmarsh)
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