留数法在计算无穷级数和的应用  

Evaluating summation of series with the resdue calculus

作　　者：杨师杰 YANG Shi-jie(Department of Physics,Beijing Normal University,Zhuhai,Guangdong 519087,China)

机构地区：[1]北京师范大学物理学系,广东珠海519087

出　　处：《大学物理》2024年第8期4-6,共3页College Physics

摘　　要：本文通过量子统计的玻色/费米分布函数,利用留数定理引入一种求无穷级数和的方法.我们采用该方法求出几种无穷级数的和,并在此基础上求得一些函数的米塔-列夫勒展开式.By employing the Bose and Fermi distribution functions,we introduce a method to calculate the summation of an infinite series via the residue calculus.With this method we obtain several infinite series sums and further derive the Mittag-Leffler expansions of some important functions.

关 键 词：留数法 玻色分布函数 无穷级数和 米塔-列夫勒展开 

分 类 号：O411[理学—理论物理]