Complex oscillation of differential polynomials in the unit disc

We consider the complex differential equations f ″ + A 1 ( z ) f ′ + A 0 ( z ) f = F and where A 0 ≢ 0, A 1 and F are analytic functions in the unit disc Δ = { z : | z | < 1}. We obtain results on the order and the exponent of convergence of zero-points in Δ of the differential polynomials g f = d 2 f ″ + d 1 f ′ + d 0 f with non-simultaneously vanishing analytic coefficients d 2 , d 1 , d 0 . We answer a question posed by J. Tu and C. F. Yi in 2008 for the case of the second order linear differential equations in the unit disc.