关键词: 微分方程, 缺项级数, 线性无关, 零点收敛指数

Abstract:

In the paper, the authors investigate the exponent of convergence of the zero-sequence of meromorphic solutions to homogeneous linear differential equation f^(k)+A_k-2f^(k-2)+…+A₁f'+A₀f=0  when its  coefficients are meromorphic functions possessing only a finite number of poles and dominant coefficient A_s(s∈{2, …, k-2})  is fabry gap. The  minimum number of linear independent transcendental solutions and the maximum number of linear independ ent transcendental solutions with finite exponents of convergence of the zero-sequence are obtained.

Key words: Differential equation, Fabry gap, Linearly independent, Exponent of convergence of zero-sequence