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.
"On the Deficiencies of Some Differential-Difference Polynomials." Abstr. Appl. Anal. 2014 (SI14) 1 - 12, 2014. https://doi.org/10.1155/2014/378151