Entire Functions and Their Derivatives Share Two Finite Sets

- Journal title : Kyungpook mathematical journal
- Volume 49, Issue 3, 2009, pp.473-481
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2009.49.3.473

Title & Authors

Entire Functions and Their Derivatives Share Two Finite Sets

Meng, Chao; Hu, Pei-Chu;

Meng, Chao; Hu, Pei-Chu;

Abstract

In this paper, we study the uniqueness of entire functions and prove the following theorem. Let n( 5), k be positive integers, and let = {z : = 1}, = {, , , }, where , , , are distinct nonzero constants. If two non-constant entire functions f and g satisfy = and = , then one of the following cases must occur: (1) f = tg, {, , , } = t{, , , }, where t is a constant satisfying = 1; (2) f(z) = , g(z) = , {, , , } = , where t, c, d are nonzero constants and = 1. The results in this paper improve the result given by Fang (M.L. Fang, Entire functions and their derivatives share two finite sets, Bull. Malaysian Math. Sc. Soc. 24(2001), 7-16).

Keywords

entire function;share set;uniqueness;

Language

English

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