Euler求和公式的一种推广和应用  

A Generalization of Euler Summation Formula and Its Applications

作　　者：刘证[1] 

机构地区：[1]鞍山科技大学理学院,辽宁鞍山114044

出　　处：《数学的实践与认识》2005年第12期157-161,共5页Mathematics in Practice and Theory

摘　　要：将只适用于有限区间上具有连续微商的函数的Eu ler求和公式推广到一般的连续函数,并应用此公式推出对于满足L ipsch itz条件的函数普通数值积分的梯形法、矩形法与S im pson法.The well-known Euler summation formula is only available for functions having continuous derivative in a finite closed interval. In this paper, a generalization of Euler summation formula for general continuous function is given and it is applied to deduce trapezoidal method, rectangular method and Simpsom method for ordinary numerical integration of functions satisfying Lipsehitz condition.

关 键 词：Euler求和公式 有界变差函数 STIELTJES积分 

分 类 号：O241.4[理学—计算数学]