The Nevanlinna and Valiron deficiencies of some \(q\)-difference-differential polynomials. (English) Zbl 1422.30052
Summary: For a zero order meromorphic function \(f(z)\), the main purpose of this paper is to investigate the value distribution on \(f\), \(f'\) and some types of \(q\)-difference-differential polynomials. We obtain some interesting results, which reveal the relation of Nevanlinna deficiencies among such functions concerning Valiron deficiency. Moreover, we give some examples to explain our conclusions.
MSC:
30D35 | Value distribution of meromorphic functions of one complex variable, Nevanlinna theory |