自然数方幂和的一种新计算方法  

A New Method of Power Sum for Natural Numbers

作　　者：乔盛元 梁亦孔 QIAO Shenyuan;LIANG Yikong(School of Urban Rail Transportation,Physics and Statistics,Shanghai University of Engineering Science,Shanghai 201620,China;School of Mathematics,Physics and Statistics,Shanghai University of Engineering Science,Shanghai 201620,China)

机构地区：[1]上海工程技术大学城市轨道交通学院,上海201620 [2]上海工程技术大学数理与统计学院,上海201620

出　　处：《上海工程技术大学学报》2020年第4期392-396,共5页Journal of Shanghai University of Engineering Science

摘　　要：研究自然数方幂和的一种函数积分和形式推广,采用泰勒展开及推广的积分中值定理等工具,给出对任意实数次幂积分形式的级数展开式.通过实例验证说明展开式具有一定的有效性.A function integral and form extension of the power sum of natural numbers was studied.By using Taylor expansion and the extended mean value theorem of integrals,the series expansion of the integral form of any real number power was given.Some examples were given to verify the effectiveness of the expansion.

关 键 词：自然数方幂和 泰勒展开 级数展开 积分中值定理 

分 类 号：O156[理学—数学]