全平面内收敛的Dirichlet级数的广义级与逼近  

The Generalize Order and Approximation of Dirichlet Series Convergent in the Whole Complex Plane

作　　者：余民权[1] 严钦波[1] 徐洪焱 YU Min-quan;YAN Qin-bo;XU Hong-yan(Jiangxi Arts&Ceramics Technology Institute,Jingdezhen 333000,China;Department of Informatics and Engineering,Jingdezhen Ceramic Institute,Jingdezhen 333403,China)

机构地区：[1]江西陶瓷工艺美术职业技术学院,江西景德镇333000 [2]景德镇陶瓷大学信息工程学院,江西景德镇333403

出　　处：《数学的实践与认识》2021年第10期247-255,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11561033);江西省自然科学基金(20181BAB201001);江西省教育厅科技项目(GJJ190876,GJJ191042,GJJ190895)。

摘　　要：通过引入两种不同形式的广义级,讨论了全平面内收敛的Dirichlet级数的增长性,得到了级数具有广义级的等价条件.此外,进一步讨论了 Dirichlet级数的逼近性质,得到了具有广义级Dirichlet级数的增长性与逼近算子,an以及λn之间的内在联系.By introducing two different concepts of the generalize order,we study the growth of Dirichlet series convergent in the whole complex plane,and obtain the conditions of Dirichlet series with generalize order.In addition,we further investigate the approximation of Dirichlet series with generalize order,and obtain some relationship about generalize order,the error,an and λn.

关 键 词：整Dirichlet级数 广义级 逼近 

分 类 号：O173[理学—数学]