On [p, q]-order of growth of solutions of complex linear differential equations near a singular point


Jianren Long, Sangui Zeng




We investigate the [p, q]-order of growth of solutions of the following complex linear differential equation f (k) + A k−1 (z) f (k−1) + · · · + A 1 (z) f + A 0 (z) f = 0, where A j (z) are analytic in C − {z 0 }, z 0 ∈ C. Some estimations of [p, q]-order of growth of solutions of the equation are obtained, which is generalization of previous results from Fettouch-Hamouda