Abstract
Let and be entire functions of order less than 1 with and transcendental. We prove that every solution of the equation , , being has zeros with infinite exponent of convergence.
Highlights
It is assumed that the reader of this paper is familiar with the basic concepts of Nevanlinna theory 1, 2 such as T r, f, m r, f, N r, f, and S r, f
Let us recall some of the previous results on the linear differential equation y e−zy B z y 0, 1.4 where B z is an entire function of finite order, When B z is polynomial, many authors 3–6 have studied the properties of the solutions of 1.4
If B z is a transcendental entire function with ρ B / 1, Gundersen 7 proved that every nontrivial solution of 1.4 has infinite order of growth
Summary
It is assumed that the reader of this paper is familiar with the basic concepts of Nevanlinna theory 1, 2 such as T r, f , m r, f , N r, f , and S r, f. Let us recall some of the previous results on the linear differential equation y e−zy B z y 0, 1.4 where B z is an entire function of finite order, When B z is polynomial, many authors 3–6 have studied the properties of the solutions of 1.4 . If B z is a transcendental entire function with ρ B / 1, Gundersen 7 proved that every nontrivial solution of 1.4 has infinite order of growth.
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