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On the Deficiencies of Some Differential-Difference Polynomials

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  • Xiu-Min Zheng
  • Hong Yan Xu

Abstract

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.

Suggested Citation

  • Xiu-Min Zheng & Hong Yan Xu, 2014. "On the Deficiencies of Some Differential-Difference Polynomials," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, February.
    • Handle: RePEc:hin:jnlaaa:378151
    DOI: 10.1155/2014/378151
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    Cited by:

    1. Hong-Yan Xu & Xiu-Min Zheng & Hua Wang, 2018. "Some Results on the Deficiencies of Some Differential-Difference Polynomials of Meromorphic Function," Mathematics, MDPI, vol. 6(10), pages 1-13, October.

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