用傅里叶级数求自然数幂和  

Summing Power Series of Natural Number by Fourier Series

作　　者：李卫高[1] 李兆强[1] 

机构地区：[1]漯河医学高等专科学校,漯河462002

出　　处：《大学数学》2014年第4期98-101,共4页College Mathematics

基　　金：漯河医学高等专科学校科研项目[2013-S-LMC15]

摘　　要：为寻求自然数幂和公式新方法,借助傅里叶级数这一解析工具,通过把幂函数xr在[0,n]上表示为傅里叶余弦级数,经过整点赋值求和,得到了自然数幂和的一个无穷级数表达式.运用此表达式进一步建立了自然数幂和问题与zeta函数之间的联系.To seek new summing method of power series of natural number, the analyzer of Fourier series is used in this paper. By means of representing the power function xγas Fourier cosine series on [0,n] , and summing assignments on the whole points, An infinite series expression of power series of natural number is obtained. Using this expression, a link between power series of natural number and Zeta function is further established.

关 键 词：自然数幂和 傅里叶级数 ZETA函数 

分 类 号：O17[理学—数学]