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On the zeros of solutions of any order of derivative of second order linear differential equations taking small functions. (English) Zbl 1340.30140

Summary: We investigate the hyper-exponent of convergence of zeros of \(f^{(j)}(z)-\varphi(z) (j\in N)\), where \(f\) is a solution of second or \(k(\geq2)\) order linear differential equation, \(\varphi(z)\not\equiv0\) is an entire function satisfying \(\sigma(\varphi)<\sigma(f)\) or \(\sigma_{2}(\varphi)<\sigma_{2}(f)\). We obtain some precise results which improve previous results. More importantly, these results also provide us a method to investigate the hyper-exponent of convergence of zeros of \(f^{(j)}(z)-\varphi(z)(j\in N)\).

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain
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