合流超几何函数的零点性质  

On the Zeros of Confluent Hypergeometric Functions

作　　者：林伟川[1] 罗旭丹 

机构地区：[1]福建师范大学数学系,福州350007 [2]Department of Applied Mathematics,University of Colorado at Boulder

出　　处：《数学物理学报（A辑）》2017年第5期801-807,共7页Acta Mathematica Scientia

基　　金：国家自然科学基金(11371225);福建省自然科学基金(2011J01006)~~

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_1F_1(α;γ;z):=∞∑n=0((α)_n)/(n!(γ)_n)z^n(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|≥Mn对所有n≥1成立.There have been many applications of confluent hypergeometric functions in quan- tum 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, oc we study the zero sets of the confluent hypergeometric function （α;γ;z）：=∞∑n=0（（α）_n）/（n!（γ）_n）z^n,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 ｜ zn｜ ≥ Mn for all n ≥ 1.

关 键 词：合流超几何函数 Jensen公式 整函数 零点列 

分 类 号：O174[理学—数学]