The Expression of Slow-Growing Meromorphic Functions Sharing One Value CM with Their Derivatives

Abstract

In this paper, we study the relations between meromorphic functions and their derivatives with one shared values, and obtain a concrete expression of meromorphic functions of zero order that share one value CM with their derivatives by a new method. Our main result is the supplementary of a related result due to Li and Yi (Li X M, Yi H X. Uniqueness of meromorphic functions sharing a meromorphic function of a small order with their derivatives. Ann. Polon. Math., 2010, 98(3): 201–219).