p级数求和的两种方法  

Two Methods of Calculating p Series

作　　者：樊龙[1] 

机构地区：[1]山西大同大学煤炭工程学院,山西大同037003

出　　处：《山西大同大学学报（自然科学版）》2016年第6期9-10,35,共3页Journal of Shanxi Datong University(Natural Science Edition)

摘　　要：当p为偶数时的情形,可采用傅里叶展开和留数定理计算求和结果:利用f(x)=x^(2k)在x=π处的傅里叶展开式可得出,留数方法在于将级数求和转化成相应某复值函数在一个闭域中的留数之和,不涉及展开式,更为简洁直观。When p is even,the result can be obtained by using Fourier series and residue theorem：we can use Fourier series of f（x） = x2k at x =π;otherwise,the advantage of residue method is the calculation can be converted to the corresponding summation of complex functions in a closed domain,more simple and intuitive than using Fourier series.

关 键 词：P级数 留数定理 傅里叶级数 

分 类 号：O175.2[理学—数学]