Growth Analysis of Meromorphic Solutions of Linear Difference Equations with Entire or Meromorphic Coefficients of Finite φ-Order

Many researchers' attentions have been attracted to various growth properties of meromorphic solution f (of finite phi-order) of the following higher order linear difference equation A(n)(z) f (z + n) + ... + A(1)(z) f (z + 1) + A(0)(z) f (z) = 0, where A(n)(z) , ..., A(0)(z) are entire or meromorphic coefficients (of finite phi-order) in the complex plane (phi : [0, infinity) -> (0, infinity) is a non-decreasing unbounded function). In this paper, by introducing a constant b (depending on phi) defined by lim/r ->infinity log r/log phi(r) = b < infinity, and we show how nicely diverse known results for the meromorphic solution f of finite phi-order of the above difference equation can be modified.