On the conditions for entire functions related to the partial theta function to belong to the Laguerre-Polya class

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:434

Article

Bohdanov, Anton¹  Vishnyakova, Anna¹ 

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

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

DOI  :  10.1016/j.jmaa.2015.09.084

来源: Elsevier

【 摘 要 】

In this paper, we study entire functions of order zero with positive Taylor coefficients and investigate sufficient or necessary conditions for such functions to have only real zeros. We answer the following question: for which values of a > 1 and m >= 1 an entire function phi(a, m)(z) = Sigma(infinity)(k=0) z(k)/a(k2)(k!)(m) and its Taylor sections belong to the Laguerre-Polya class? (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free