On a necessary condition for an entire function with the increasing second quotients of Taylor coefficients to belong to the Laguerre-Polya class

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:480

Article

Thu Hien Nguyen¹  Vishnyakova, Anna¹ 

[1] Kharkov Natl Univ, Dept Math & Comp Sci, 4 Svobody Sq, UA-61022 Kharkov, Ukraine

关键词: Lagucrre-Polya class;    Entire functions of order zero;    Real-rooted polynomials;    Multiplier sequences;    Complex zero decreasing sequences;   

DOI  :  10.1016/j.jmaa.2019.123433

来源: Elsevier

【 摘 要 】

For an entire function f(z) = Sigma(infinity)(k=0) a(k)z(k), a(k) > 0, we show that f does not belong to the Laguerre-Polya class if the quotients a(n-1)(2)/a(n)-2a(n) are increasing in n, and c := lim(n ->infinity) a(n-1)(2)/a(n)-2a(n) is smaller than an absolute constant q(infinity) (q(infinity) approximate to 3.2336). (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free