ENTIRE FUNCTIONS REPRESENTED BY LAPLACE-STIELTJES TRANSFORMS CONCERNING THE APPROXIMATION AND GENERALIZED ORDER  

作　　者：Hongyan XU Yinying KONG 徐洪焱;孔荫莹(School of Mathematics and Computer Science,Shangrao Normal University,Shangrao 334001,China;Research Institute of Innovation Competitiveness of Guangdong,HongKong and Macao Bay Area(RHC),Guangdong University of Finance and Economics,Guangzhou 510320,China)

机构地区：[1]School of Mathematics and Computer Science,Shangrao Normal University,Shangrao 334001,China [2]Research Institute of Innovation Competitiveness of Guangdong,HongKong and Macao Bay Area(RHC),Guangdong University of Finance and Economics,Guangzhou 510320,China

出　　处：《Acta Mathematica Scientia》2021年第2期646-656,共11页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (11561033);the Natural Science Foundation of Jiangxi Province in China (20181BAB201001);the Foundation of Education Department of Jiangxi (GJJ190876, GJJ190895,GJJ202303) of China;supported by Guangdong Natural Science Foundation(2018A030313954);Guangdong University (New Generation Information Technology) Key Field Project(2020ZDZX3019);Project of Guangdong Province Innovative Team (2020WCXTD011);Guangdong Provincial Government’s project “Promoting the construction of the Guangdong-Hong Kong-Macao Greater Bay Area and building a new open economic system”.

摘　　要：The first aim of this paper is to investigate the growth of the entire function defined by the Laplace-Stieltjes transform converges on the whole complex plane.By introducing the concept of generalized order,we obtain two equivalence theorems of Laplace-Stiettjes transforms related to the generalized order,A_(n)^(*)andλ_(n).The second purpose of this paper is to study the problem on the approximation of this Laplace-Stieltjes transform.We also obtain some theorems about the generalized order,the error,and the coefficients of Laplace-Stieltjes transforms,which are generalization and improvement of the previous results.

关 键 词：Laplace-Stieltjes transform order ERROR GROWTH 

分 类 号：O174[理学—数学]