張立柱

(上海財(cái)經(jīng)大學(xué)應(yīng)用數(shù)學(xué)系,上海 200433)

級(jí)數(shù)的常規(guī)可和,Cesàro可和與Abel可和的幾點(diǎn)討論

張立柱

(上海財(cái)經(jīng)大學(xué)應(yīng)用數(shù)學(xué)系,上海 200433)

討論級(jí)數(shù)常規(guī)可和、Cesàro可和與Abel可和的關(guān)系.利用數(shù)學(xué)分析級(jí)數(shù)理論,證明Abel可和適用范圍最廣,Cesàro可和其次,級(jí)數(shù)常規(guī)可和適用范圍最小.這個(gè)結(jié)論豐富了經(jīng)典級(jí)數(shù)理論,為實(shí)際應(yīng)用中選用合適可和提供依據(jù).

級(jí)數(shù)常規(guī)可和;Cesàro可和;Abel可和

1 引言

2 理論探討與結(jié)果

3 結(jié)論

本文研究了級(jí)數(shù)的常規(guī)可和,Cesàro可和與Abel可和的關(guān)系,證明了常規(guī)可和是Cesàro可和的特例,而Cesàro可和又是Abel可和的特例,從而可知從適用范圍而言,Abel可和適用范圍最廣,Cesàro可和適用范圍其次,常規(guī)可和適用范圍最小.

[1]陳紀(jì)修.數(shù)學(xué)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.

國(guó)家自然科學(xué)基金(11201284).

張立柱(1973-),博士,副教授,研究方向：計(jì)算流體力學(xué)，數(shù)學(xué)分析.

2010 MSC:40C99