合流超几何函数的零点性质

数学物理学报 ›› 2017, Vol. 37 ›› Issue (5): 801-807.

• 论文 • 下一篇

合流超几何函数的零点性质

林伟川¹, 罗旭丹²

1. 福建师范大学数学系福州 350007;
2. Department of Applied Mathematics, University of Colorado at Boulder, Colorado, USA

收稿日期:2016-12-17 修回日期:2017-05-21 出版日期:2017-10-26 发布日期:2017-10-26
作者简介:林伟川,E-mail:sxlwc936@fjnu.edu.cn;罗旭丹,E-mail:lxdmathematics@gmail.com
基金资助:
国家自然科学基金（11371225）和福建省自然科学基金（2011J01006）

On the Zeros of Confluent Hypergeometric Functions

Lin Weichuan¹, Luo Xudan²

1. Department of Mathematics, Fujian Normal University, Fuzhou 350007;
2. Department of Applied Mathematics, University of Colorado at Boulder, Colorado, USA

Received:2016-12-17 Revised:2017-05-21 Online:2017-10-26 Published:2017-10-26
Supported by:
Supported by the NSFC (11371225) and the Natural Science Foundation of Fujian Province (2011J01006)

摘要/Abstract

摘要：

合流超几何函数在量子力学和统计学中被广泛应用，尤其在数学物理学中的许多问题可以借助此函数的零点位置性质来解决.该文对合流超几何函数
1F₁（α；γ；z）：=zⁿ（α，γ，γ-α∉Z_≤0）
的零点集进行研究，证明了如果{z_n}_n=1^∞是F（α；γ；z）按其模增序排列的零点集，其中重级零点按其重数计算，则存在常数M>0使得|z_n|≥ M_n对所有n ≥ 1成立.

关键词: 合流超几何函数, Jensen公式, 整函数, 零点列

Abstract:

There have been many applications of confluent hypergeometric functions in quantum mechanics and statistics. Furthermore, many problems in mathematical physics can be solved with the help of the location of zeros of confluent hypergeometric functions. In this paper, we study the zero sets of the confluent hypergeometric function 1F₁(α;γ;z):=zⁿ, where α,γ,γ-α∉Z_{≤ 0}, and show that if {z_n}_n=1^∞ is the zero set of F(α;γ;z) with multiple zeros repeated and modulus in increasing order, then there exists a constant M > 0 such that|z_n|≥ M_n for all n ≥ 1.

Key words: Confluent hypergeometric functions, Jensen Formula, Entire function, Zerosequence

中图分类号:

O174

林伟川, 罗旭丹. 合流超几何函数的零点性质[J]. 数学物理学报, 2017, 37(5): 801-807.

Lin Weichuan, Luo Xudan. On the Zeros of Confluent Hypergeometric Functions[J]. Acta mathematica scientia,Series A, 2017, 37(5): 801-807.

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合流超几何函数的零点性质

On the Zeros of Confluent Hypergeometric Functions

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