| 翻訳と辞書 |
| antiholomorphic function ： ウィキペディア英語版 |
antiholomorphic function
In mathematics, antiholomorphic functions (also called antianalytic functions) are a family of functions closely related to but distinct from holomorphic functions.
A function of the complex variable z defined on an open set in the complex plane is said to be antiholomorphic if its derivative with respect to exists in the neighbourhood of each and every point in that set, where is the complex conjugate.
One can show that if ''f''(''z'') is a holomorphic function on an open set ''D'', then ''f''() is an antiholomorphic function on , where is the reflection against the ''x''-axis of ''D'', or in other words, is the set of complex conjugates of elements of ''D''. Moreover, any antiholomorphic function can be obtained in this manner from a holomorphic function. This implies that a function is antiholomorphic if and only if it can be expanded in a power series in in a neighborhood of each point in its domain.
If a function is both holomorphic and antiholomorphic, then it is constant on any connected component of its domain.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「antiholomorphic function」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|