级数的常规可和,Cesàro可和与Abel可和的几点讨论

张立柱

(上海财经大学应用数学系,上海 200433)

级数的常规可和,Cesàro可和与Abel可和的几点讨论

张立柱

(上海财经大学应用数学系,上海 200433)

讨论级数常规可和、Cesàro可和与Abel可和的关系.利用数学分析级数理论,证明Abel可和适用范围最广,Cesàro可和其次,级数常规可和适用范围最小.这个结论丰富了经典级数理论,为实际应用中选用合适可和提供依据.

级数常规可和;Cesàro可和;Abel可和

1 引言

2 理论探讨与结果

3 结论

本文研究了级数的常规可和,Cesàro可和与Abel可和的关系,证明了常规可和是Cesàro可和的特例,而Cesàro可和又是Abel可和的特例,从而可知从适用范围而言,Abel可和适用范围最广,Cesàro可和适用范围其次,常规可和适用范围最小.

[1]陈纪修.数学分析[M].北京:高等教育出版社,2004,14:186-188.

[2]Stein E M,Shakarchi R.Fourier Analysis,an Introduction[M].Princeton:Princeton Univ.Press,2011.

[3]Bender C M.Advanced Mathematical Methods for Scientists and Engineers[M].New York:McGraw-Hill, 1978.

[4]Ibrahim Canak,Umit Totur.A condition under which slow oscillation of a sequence follows from Cesàro summability of its generator sequence[J].Applied Mathematics and Computation,2010,216:1618-1623.

[5]Ibrahim Canak.A theorem on the Cesàro summability method[J].Computers and Mathematics with Applications,2011,61:1162-1166.

[6]Ferenc Weisz.Cesàro summability of higher dimensional Fourier series[J].Annales Univ.Sci.Budapest., Sect.Comp.,2012,37:47-64.

[7]Jonathan Sondow.Analytic continuation of Riemann′s Zeta function and values at negative integers via Euler′s Transformation of Series[J].Proceedings of the American Mathematical Society,1994,102(2):421-424.

Some notes on series standard summability,Cesàro summability and Abel summability

Zhang Lizhu

(Department of Applied Mathematics,Shanghai University of Finance and Economics, Shanghai200433,China)

The relationship among series standard summability,Cesàro summability and Abel summability is studied in this paper.By using series theory in mathematical analysis,it is proved that Abel summability is the strongest,and Cesàro summability is stronger than the standard summability.The conclusion enriches the classic series theory,and provides theory basis for choosing suitable summability in practical applications.

series standard summability,Cesàro summability,Abel summability

O173.1

A

1008-5513(2013)06-0565-07

10.3969/j.issn.1008-5513.2013.06.003

2013-08-09.

国家自然科学基金(11201284).

张立柱(1973-),博士,副教授,研究方向：计算流体力学，数学分析.

2010 MSC:40C99