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.
Complex difference; value distribution; Borel exceptional value
ZHANG, RANRAN and CHEN, ZONGXUAN
"Value distribution of meromorphic functions and their differences,"
Turkish Journal of Mathematics: Vol. 36:
3, Article 6.
Available at: https://journals.tubitak.gov.tr/math/vol36/iss3/6