文档介绍：摘要
本文通过对大量国内外复数域中多值函数的相关研究资料收集和归纳整理, 从简单到复杂对多值函数的解析理论研究, :定义法、分类讨论法、限制辐角法、;本文对复数辐角的变化特性进行了分类讨论,从而加深了辐角多值性的理解,,详细论述了多值函数的各单值解析分支的关键问题及其方法;除此之外,本文还利用多值函数来计算解析函数的积分,将解析函数泰勒展开成幂级数以及多值函数的变化特性——共形映射.
关键词:辐角;多值函数;单值解析分支;共形映射
ABSTRACT
This article on the large multi-valued function plex field research data collection and synthesis, from simple plex multi-valued function analytic theory, make plex field of multiple-valued function as a systematic theory of knowledge. Paper give some determination methods on a multi-valued function of plex field : the definition, classification and discussion of law, limiting convergence angle method, cut plane. and determine the method of its corresponding example; this change on the polar angle characteristics plex were classified and discussed in order to enhance the convergence angle more than the value of understanding as the basis for in-depth analysis of the value of multi-valued function over the nature of reason. to radical functions, and logarithmic functions as the primary representative of the typical multi-valued function in detail discusses the multi-valued function of the single-valued analytic branch of the key issues and methods; In addition, we use the multi-value function to calculate the integral analytic functions, and will expand into a Taylor power series of analytic functions and multi-valued function change characteristics - Conformal mapping.
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Keywords: Argument ; multi-valued function ; single-valued analytic branch ; conformal mapping
目录
前言 1页
第一章复数辐角的多值性 2页
2页
3页
第二章初等多值函数的多值解析性 5页
5页
5页
7页
10页
10页
11页
12页
13页
13页
第三章多值解析函数的积分与幂级数的表示法 15页第四章多值函数的共形映射 17页
(n为大于1的整数) 17页
18页
第五章结论 20页
参考文献 21页
致谢