Uniqueness and value-sharing of entire functions
In this paper, we study the uniqueness of entire functions and prove the following theorem. Let f(z) and g(z) be two nonconstant entire functions, n, k two positive integers with n > 2k + 4. If [f(n) (z)]((k)) and [g(n) (z)]((k)) share 1 with counting the multiplicity, then either f(z) = c(1)e(cz), g(z) = c(2)e(-cz), where c(1), c(2), and c are three constants satisfying (-1)(k) (c(1)c(2))(n) (nc)(2k) = 1, or f (z) drop tg(z) for a constant t such that t(n) = 1. (C) 2002 Elsevier Science Ltd. All rights reserved.
entire function sharing value differential polynomial