Entire solutions of higher order Briot-Bouquet equations
Alexandre Eremenko, Tuen Wai Ng, Teng Zhang
Abstract
For a meromorphic function f in the complex plane, we determine when f and f(k) are algebraically dependent. This happens precisely when f belongs to the class W of elliptic functions and their degenerates, or satisfies a linear differential equation f(k) + af + b = 0 with constant coefficients. The case of functions having a pole was settled previously. We complete the proof by treating entire solutions.
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