无限级Laplace-Stieltjes变换所表示的整函数的增长性与逼近

数学物理学报 ›› 2020, Vol. 40 ›› Issue (3): 556-568.

无限级Laplace-Stieltjes变换所表示的整函数的增长性与逼近

徐洪焱^1,^2,*(),刘三阳²

¹ 上饶师范学院数学与计算机学院江西上饶 334001
² 西安电子科技大学数学与统计学院西安 710126

收稿日期:2019-04-23 出版日期:2020-06-26 发布日期:2020-07-15
通讯作者: 徐洪焱 E-mail:xhyhhh@126.com
基金资助:
国家自然科学基金(11561033);国家自然科学基金(61877046);江西省自然科学基金(20181BAB201001);江西省教育厅科学技术项目(GJJ180734);江西省教育厅科学技术项目(GJJ180735)

The Approximation and Growth of Entire Function Represented by Laplace-Stieltjes Transform with Infinite Order

Hongyan Xu^1,^2,*(),Sanyang Liu²

¹ School of Mathematics and Computer Science, Shangrao Normal University, Jiangxi Shangrao 334001
² School of Mathematics and Statistics, Xidian University, Xi'an 710126

Received:2019-04-23 Online:2020-06-26 Published:2020-07-15
Contact: Hongyan Xu E-mail:xhyhhh@126.com
Supported by:
the NSFC(11561033);the NSFC(61877046);the NSF of Jiangxi Province(20181BAB201001);the Foundation of Education Department of Jiangxi(GJJ180734);the Foundation of Education Department of Jiangxi(GJJ180735)

摘要/Abstract

摘要：

通过引入双下q-型的概念，讨论了具有非正规增长的全平面收敛的Laplace-Stieltjes变换的增长性与逼近，得到了Laplace-Stieltjes变换的尾项与双下q-型，A_n^*以及λ_n的关系定理，推广了罗茜，孔荫莹，Singhal与Srivastava等的结果.

关键词: Laplace-Stieltjes变换, 逼近, q-非正规增长

Abstract:

The main purpose of this article is to investigate the growth and approximation of Laplace-Stieltjes transform with irregular growth converges in the whole plane, by introducing the concept of the double lower q-type. We obtain some relation theorems concerning the double lower q-type, the error, A_n^* and λ_n, which are extension and improvement of the previous theorems given by Luo-Kong, Singhal-Srivastava.

Key words: Laplace-Stieltjes transform, Approximation, Double lower q-type

中图分类号:

O174

徐洪焱,刘三阳. 无限级Laplace-Stieltjes变换所表示的整函数的增长性与逼近[J]. 数学物理学报, 2020, 40(3): 556-568.

Hongyan Xu,Sanyang Liu. The Approximation and Growth of Entire Function Represented by Laplace-Stieltjes Transform with Infinite Order[J]. Acta mathematica scientia,Series A, 2020, 40(3): 556-568.

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