On the entire functions from the Laguerre-Polya I class having the increasing second quotients of Taylor coefficients

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:498

Article

Thu Hien Nguyen¹  Vishnyakova, Anna¹ 

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

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

DOI  :  10.1016/j.jmaa.2021.124955

来源: Elsevier

【 摘 要 】

We prove that if f(x) = Sigma(infinity)(k=0) a(k)x(k), a(k) > 0, is an entire function such that the sequence Q := (a(k)(2)/a(k-1)a(k+1))(k=1)(infinity) is non-decreasing and a(1)(2)/a(0)a(2) >= 2(3)root 2, then all but a finite number of zeros of f are real and simple. We also present a criterion in terms of the closest to zero roots for such a function to have only real zeros (in other words, for belonging to the Laguerre-Polya class of type I) under additional assumption on the sequence Q. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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