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On oscillation theorems for differential polynomials. (English) Zbl 1183.34135
Summary: We investigate the relationship between small functions and differential polynomials \(g_{f}\left( z\right)=d_{2}f^{^{\prime \prime }} + d_{1}f^{^{\prime }}+d_{0}f\), where \(d_0, d_1, d_2\) are meromorphic functions that are not all equal to zero with finite order generated by solutions of the second order linear differential equation
\[ f''+Af'+Bf=F, \]
where \(A,B,F\not\equiv 0\) are finite order meromorphic functions having only finitely many poles.

MSC:
34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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