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Entire solutions of higher order Briot-Bouquet equations
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
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