摘要
Laurent展式是复变函数奇点分类的重要工具,也是留数计算的主要方法之一,求其展式常用间接方法.文章使用Laurent定理的直接展开方法与复积分技巧,首先把一类双曲余弦函数Laurent展式及系数恒等式推广到整函数中.然后,针对奇、偶整函数,得到两类Laurent展式及相应系数恒等式.最后,证明了复指数函数相应的两类Laurent展式与系数恒等式.
Laurent expansion is an important tool for the classification of singularities of complex functions and also one of the main methods for residue calculation.The indirect method is often used to find its expansion.In this article,we employ the direct expansion method of Laurent theorem and the technique of complex integration to first extend the Laurent expansion and coefficient identity of a class of hyperbolic cosine functions to the entire function.Then,for odd and even integer functions,two types of Laurent expressions and the corresponding coefficient identities are obtained.Finally,two types of Laurent expressions and coefficient identities corresponding to complex exponential functions were proved.
作者
储亚伟
李冰艳
丁雨韩
CHU Yawei;LI Bingyan;DING Yuhan(Fuyang Normal University,Fuyang 236037,China;Fuyang University of Technolog,Fuyang 236000,China)
出处
《通化师范学院学报》
2026年第2期56-60,共5页
Journal of Tonghua Normal University
基金
国家级大学生创新训练项目(202410371030)
安徽省重大教学研究项目(2024jyxm0311)
安徽省“AI+教育”课程项目(2024aijy242)
安徽省大学生创新训练项目(S202510371010,S202510371063)
阜阳师范大学协同提质教学团队项目(2024XTTZTD01),阜阳师范大学教学研究项目(2024BBXTJY04,2024JYXM0001)。
