Abstract and Applied Analysis

On the Deficiencies of Some Differential-Difference Polynomials

Xiu-Min Zheng and Hong Yan Xu

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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.

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Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 378151, 12 pages.

First available in Project Euclid: 6 October 2014

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Zheng, Xiu-Min; Xu, Hong Yan. On the Deficiencies of Some Differential-Difference Polynomials. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 378151, 12 pages. doi:10.1155/2014/378151. https://projecteuclid.org/euclid.aaa/1412607233

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