﻿ 两类形式幂级数的递推公式 The Recursive Formula of Two Kinds of Formal Power Series

Pure Mathematics
Vol.04 No.04(2014), Article ID:13855,7 pages
10.12677/PM.2014.44020

The Recursive Formula of Two Kinds of Formal Power Series

Yanli Chen, Wanhui Ji

Yinchuan Energy Institute, Yinchuan

Email: chenyanli8866.hi@163.com

Received: Jun. 10th, 2014; revised: Jul. 8th, 2014; accepted: Jul. 16th, 2014

Copyright © 2014 by authors and Hans Publishers Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY).

http://creativecommons.org/licenses/by/4.0/

ABSTRACT

By using the trigonometric function, the hyperbolic function and the series expansion of their product, the expansions and the recursive formula of these two forms of power series [(’s ratio of secx series) and (’s ratio of secxsechx series )] are derived. At the same time, we prove them one by one using the residue theorem.

Keywords:Series of Trigonometric Function, Formal Power Series, Recursive Formula, Residue Theorem

Email: chenyanli8866.hi@163.com

1. 引言

[级数的系数]的表达式和递推公式，并应用留数基本定理逐一作出证明。

(1)

(2)

(3)

2. 和式的计算

2.1. 考虑围线积分

Figure 1. Rectangular area in the complex plane

2.3. 考虑围线积分

3. 和式计算

3.1. 考虑围线积分

3.2. 考虑围线积分

3.3. 考虑围线积分

The Recursive Formula of Two Kinds of Formal Power Series. 理论数学,04,130-137. doi: 10.12677/PM.2014.44020

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