Abstract
Brück’s conjecture asserts that if a non-constant entire function f(z) with hyper-order \(\rho _{2}(f) \not \in \mathbb {N}\cup \{\infty \}\) shares one finite value a CM (counting multiplicities) with its derivative, then \(f'-a=c(f-a)\), for some non-zero constant c. This conjecture has been affirmed for entire functions with finite order and hyper-order less than one. In this paper, we show that Brück’s conjecture is true for entire functions that satisfy second order differential equations with meromorphic coefficients of finite order.
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The authors are grateful to the referee for his careful reading of the manuscript and for the valuable suggestions.
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Dida, R., El Farissi, A. Brück’s Conjecture for Solutions of Second-Order Complex ODE. Mediterr. J. Math. 21, 114 (2024). https://doi.org/10.1007/s00009-024-02642-z
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DOI: https://doi.org/10.1007/s00009-024-02642-z