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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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