Taiwanese Journal of Mathematics

ENTIRE FUNCTIONS AND THEIR HIGHER ORDER DIFFERENCES

Chuang-Xin Chen and Zong-Xuan Chen

Full-text: Open access

Abstract

In this paper, we prove that for a transcendental entire function $f(z)$ of finite order such that $\lambda(f-a(z))\lt \sigma(f)$, where $a(z)$ is an entire function and satisfies $\sigma(a(z))\lt 1$, $n$ is a positive integer, if $\Delta_{\eta}^nf(z)$ and $f(z)$ share entire function $b(z)\,(\,b(z)\not\equiv a(z))$ satisfying $\sigma(b(z))\lt 1$ CM, where $\eta\,(\in\mathbb{C})$ satisfies $\Delta_{\eta}^nf(z)\not\equiv 0$, then $$f(z)=a(z)+ce^{c_1z},$$ where $c,\,c_1$ are two nonzero constants.

Article information

Source
Taiwanese J. Math., Volume 18, Number 3 (2014), 711-729.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706436

Digital Object Identifier
doi:10.11650/tjm.18.2014.3453

Mathematical Reviews number (MathSciNet)
MR3213382

Zentralblatt MATH identifier
1357.39012

Subjects
Primary: 39A10: Difference equations, additive 30D35: Distribution of values, Nevanlinna theory

Keywords
complex difference meromorphic function Borel exceptional value sharing value

Citation

Chen, Chuang-Xin; Chen, Zong-Xuan. ENTIRE FUNCTIONS AND THEIR HIGHER ORDER DIFFERENCES. Taiwanese J. Math. 18 (2014), no. 3, 711--729. doi:10.11650/tjm.18.2014.3453. https://projecteuclid.org/euclid.twjm/1499706436


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