Value distribution of meromorphic functions and their differences

Abstract

Let f(z) be a transcendental meromorphic function. Results are proved concerning the value distribution of the n'th forward difference \Delta^nf(z), in terms of Borel exceptional values of f(z). The results may be partly viewed as discrete analogues of a classical theorem of Hayman dealing with the possible relationships between Picard exceptional values of f(z) and its derivatives.