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 d-4. If [fn(z)](k) and [gn(z)](k) share 1 with counting the multiplicity, then either f(z) = Cl ecz, g(z) = c2e -c
Uniqueness of entire functions
โ Scribed by Jianming Chang; Mingliang Fang
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 195 KB
- Volume
- 288
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
โฆ Synopsis
Let f be a nonconstant entire function and let a be a meromorphic function satisfying
and a โก a is necessary. This extended a result due to Jank, Mues and Volkmann.
๐ SIMILAR VOLUMES
This paper studies uniqueness problems on entire functions that share a finite nonzero value counting multiplicities with their derivatives and gives a proper ลฝ answer to the problem proposed by L. Z. Yang ''Proceedings of the 6th Interna-. tional Colloquium on Complex Analysis, 1998,'' pp. 176แ183
This paper is devoted to studying the uniqueness problem of entire functions sharing one value or fixed points. We improve some results given by Fang and extend some results given by Fang and Qiu and by Lin and Yi.