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Abstract and Applied Analysis
Volume 2014, Article ID 378151, 12 pages
Research Article

On the Deficiencies of Some Differential-Difference Polynomials

1Institute of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China
2Department of Informatics and Engineering, Jingdezhen Ceramic Institute, Jingdezhen 333403, China

Received 1 November 2013; Accepted 4 January 2014; Published 27 February 2014

Academic Editor: Zong-Xuan Chen

Copyright © 2014 Xiu-Min Zheng and Hong Yan Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The characteristic functions of differential-difference polynomials are investigated, and the result can be viewed as a differential-difference analogue of the classic Valiron-Mokhon’ko Theorem in some sense and applied to investigate the deficiencies of some homogeneous or nonhomogeneous differential-difference polynomials. Some special differential-difference polynomials are also investigated and these results on the value distribution can be viewed as differential-difference analogues of some classic results of Hayman and Yang. Examples are given to illustrate our results at the end of this paper.