On the Orders and Zeros of Solutions of a Class of Entire Function Linear Differential Equations

摘要

This paper is based on the theorem of entire function solutions: each nontrivial solution f of the differential equation f''+F(z)f'+G(z)f = 0 has an infinite order. The study expands its assumptions and allows some coefficients to have the equal order to prove that series of the whole transcendental solution approaches to infinity, which is to solve the order and the convergence of the zero of fSUP(k)/SUP + ASUBK-1/SUBfSUP(k-1)+... + ASUB0/SUBf/SUP = 0.