級數的常規可和,Cesàro可和與Abel可和的幾點討論

張立柱

(上海財經大學應用數學系,上海 200433)

級數的常規可和,Cesàro可和與Abel可和的幾點討論

張立柱

(上海財經大學應用數學系,上海 200433)

討論級數常規可和、Cesàro可和與Abel可和的關系.利用數學分析級數理論,證明Abel可和適用范圍最廣,Cesàro可和其次,級數常規可和適用范圍最小.這個結論豐富了經典級數理論,為實際應用中選用合適可和提供依據.

級數常規可和;Cesàro可和;Abel可和

1 引言

2 理論探討與結果

3 結論

本文研究了級數的常規可和,Cesàro可和與Abel可和的關系,證明了常規可和是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,常規可和適用范圍最小.

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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.

國家自然科學基金(11201284).

張立柱(1973-),博士,副教授,研究方向：計算流體力學，數學分析.

2010 MSC:40C99