用泰勒定理推广一类积分恒等式
Generalization of a Class of Integral Identities by Taylor's Theorem
储亚伟 1徐秀银 1叶薇薇 1李雯雯1
作者信息
- 1. 阜阳师范大学数学与统计学院(安徽 阜阳 236037)
- 折叠
摘要
借助复积分可以解决一些复杂实积分的计算问题,该文使用解析函数泰勒定理中泰勒系数的不同形式和复积分的计算技巧,从五个方面推广了一类同时含有三角函数与指数函数或双曲函数的实积分恒等式,并证明了一类含有不同角度余弦函数有理分式的积分恒等式,为复杂实积分的计算与复积分的应用提供了新的思路与案例,丰富了应用留数定理计算实积分的内容.
Abstract
Some complex real integrals can be solved by means of complex integrals.Using the different forms of Taylor coefficient in Taylor theorem of analytic function and the calculation techniques of com-plex integral,this paper generalizes a class of real integral identities containing trigonometric functions,exponential functions or hyperbolic functions from five aspects,and proves a class of integral identities containing rational fractions of cosine functions of different angles.This provides new ideas and cases for the calculations of complex real integrals and the applications of complex integration.
关键词
泰勒定理/泰勒系数/复积分/留数定理/积分恒等式/推广Key words
Taylor theorem/Taylor coefficient/complex integral/residue theorem/integral identity/gener-alize引用本文复制引用
出版年
2024
NETL
NSTL
万方数据