复合函数的孤立奇点与留数计算

复合函数的孤立奇点与留数计算

摘要

复合函数的孤立奇点与留数计算是留数理论应用中的重要内容，对于1些复杂的复合函数，如果直接讨论其孤立奇点的类型与留数计算往往极为困难，为了解决这1问题，本文将复合函数分解为两个简单函数来研究，首先建立了复合函数的孤立奇点类型与其内外函数的孤立奇点类型的关系，在1定意义下，所得结果具有普遍性。然后，根据某些孤立奇点的特性，并利用留数的定义，建立了若干个用内外函数的留数或某些Laurent系数来表示复合函数的留数的公式，并举例介绍了其应用，从列举的例子中可以看到所得公式在简化复合函数留数计算中的作用。

关键词：复合函数，孤立奇点，可去奇点，极点，本性奇点，留数。

Abstract

Compound functions isolated singularity and residue computation is the substantial content of residue theorys application, to several complicated compound function, if we discuss it directly, it is difficulty. To solve this problem, this passage will put compound function into two parts. Firstly, constitute compound functions isolated singularity and relation of interior function and external function. In a degree, the result is ripeness. Where after. We can use certain isolated singularitys property and define of fluxion, constitute several interior function and external functions fluxion or several Laurent quotient to show compound functions flexion’s expressions. Take some example to solve compound function.

Key words: Compound function, isolated singularity, removable singularity, vertex, essential singularity, residue.