含参数的Basel级数的和及其应用  

Sum of Basel Series with Parameters and Application

作　　者：孔庆海[1] KONG Qinghai(Department of Mathematics, School of Science, Northeastern University, Shenyang 110819, China)

机构地区：[1]东北大学理学院数学系,辽宁沈阳110819

出　　处：《高等数学研究》2022年第3期52-53,63,共3页Studies in College Mathematics

摘　　要：利用Fourier级数及其和函数给出了含参数的巴塞尔级数的和,作为应用得到了一系列的特殊级数的和,最后验证了含参数的巴塞尔级数的和即是巴塞尔级数的和的推广.By using Fourier series and its sum function,the sum of Basel series with parameters is given.As an application,the sums of many special series are obtained.It is verified that the sum of the Basel series with parameters generalizes the sum of Basel series.

关 键 词：FOURIER级数 Basel级数 和函数 交错级数 收敛. 

分 类 号：O173.1[理学—数学]