复变量正余弦函数的公理化(等价)定义

Axiomatic Definition of (Co)sine with Complex Variables

此文给出了复变量情形正、余弦函数的公理化定义(等价定义),它们具有公理化数学定义所具有的形式简洁,本质属性清晰,便于解析推演等优点。由于复变量正、余弦函数在复变量初等函数乃致整个复变函数(类)中的基本重要性,文章的讨论对相应数学分支的讨论是有参考价值的。当然,若将此文的R2(复数域)限制为R1(实数域),则(特殊地)适于实变量正、余弦函数的讨论。

This paper illustrates the axiomatic definition of （co） sine with complex variables which is of simple form, distinct attribute and easy to analyze and manipulate. This discussion is of reference value to relevant mathematic branches owing to the importance of （co） sine with complex variables in this field. Yet if R2 in this paper is confined to R1, special field can apply to （co）sine with real variables.