广义Laplace-Stieltjes变换所表示整函数的β级和广义型  

TheβOrder and Generalized Type of Entire Functions Represented by Generalized Laplace-Stieltjes Transforms

作　　者：宁菊红[1] 宋文佩 黄文平 NING Juhong;SONG Wenpei;HUANG Wenping(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang Jiangxi 330022,China;Suzhouwan Experimental Junior Middle School,Suzhou Jiangsu 215200,China;Basic Department,Army Infantry College,Nanchang Jiangxi 330103,China)

机构地区：[1]江西师范大学数学与统计学院,江西南昌330022 [2]苏州湾初级实验中学,江苏苏州215200 [3]陆军步兵学院基础部数学教研室,江西南昌330103

出　　处：《江西师范大学学报（自然科学版）》2020年第6期590-593,共4页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11661044)资助项目.

摘　　要：该文研究了由广义Laplace-Stieltjes变换所表示的整函数的增长性.首先介绍了由广义Laplace-Stieltjes变换所表示的整函数在圆周上的最大模、最大项的定义;其次研究并得到了由最大模、最大项所表示的整函数的β级、广义型和用An、λn所表示的整函数的β级、广义型之间的等价关系;最后给出了定理的相应推论,得到了Laplace-Stieltjes变换所表示的整函数在圆周上的β级、广义型.The growth of the entire function represented by the generalized Laplace-Stieltjes transform is studied in this paper.Firstly,the definition of the maximum modulus and maximum term of the entire function is introduced.Secondly,the equivalence relation between theβorder,generalized type of the entire function represented by the maximum modulus and maximum term and theβorder,generalized type of the entire function represented by An、λn is studied and obtained.Finally,the corresponding corollaries of the theorem are given.Theβorder and generalized type of the entire function represented by Laplace-Stieltjes transform on the circumference are obtained.

关 键 词：整函数 广义Laplace-Stieltjes变换 最大模 最大项 β级 广义型 

分 类 号：O174.52[理学—数学]