关于欧拉—马克劳林求和公式的应用研究  

The Euler-Maclaurin Summation Formula and It's Application

作　　者：杨倩丽[1] 车雨红[1] Yang Qianli Che Yuhong(School of Mathematics and Physics, Weinan Normal University, Weinan Shaanxi 714099)

机构地区：[1]渭南师范学院数理学院,陕西渭南714099

出　　处：《首都师范大学学报（自然科学版）》2016年第6期13-17,9,共6页Journal of Capital Normal University：Natural Science Edition

基　　金：陕西省自然科学基金资助项目(2013JM1016;2014JM1026);渭南师范学院校级项目(15YKP015);陕西省民间军事一体化研究项目(15JMR19);陕西省教育厅课题(16JK1265)

摘　　要：研究了欧拉—马克劳林求和公式,目的是推广欧拉—马克劳林求和公式的应用;采用了数论特殊函数和解析数论相结合的方法;通过欧拉—马克劳林求和公式给出了三个重要的结论,通过伯努利级数和欧拉常数表示了n∑1,利用伯努利级数和伯努利多项式积分得出并证明了重要结论ψ(x)和ζ(u,a);这些结论对于数论特殊函k=1k数的研究具有重要作用.Euler-Maclaurin Summation Formula was been researched, the purpose was to promote the application of it. The innovation of method was combination with number theory special function and analytic number theory. Threeimportant resuhs were gotten by the Euler-Maclaurin Summation Formula, n∑k=1 1/k was expressed by Bernoulli seriesand Euler-Maclaurin, ψ（x） and Hurwitz Zeta-functionξ（u,a）were stated and proved by Bernoulli series and integral of Bernoulli polynomials. It was very important to research the number theory special function.

关 键 词：欧拉—马克劳林求和 赫维茨ξ函数 伯努利级数 对数导数 

分 类 号：O156.4[理学—数学]