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

[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.

[发布日期] 2019-12-15

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