Some Results on the Complex Oscillation Theory of Differential Equations with Polynomial Coefficients

Abstract

In this paper, we study the possible orders of transcendental solutions of the differential equation f(n) + an−1 (z) f(n−1) + · · · + a1 (z) f0 + a0 (z) f = 0, where a0 (z) , . . . , an−1 (z) are nonconstant polynomials. We also investigate the possible orders and exponents of convergence of distinct zeros of solutions of non-homogeneous differential equation f(n) +an−1 (z) f(n−1) +· · ·+a1 (z) f0 + a0 (z) f = b (z) , where a0 (z) , . . . , an−1 (z) and b (z) are nonconstant polynomials. Several examples are given.