Abstract
In this note, the relationship between a non-constant entire function $f$ and its linear differential polynomial $L(f)$ has been obtained when they share two finite values, ignoring multiplicities, by applying value distribution theory. This confirms Frank's conjecture as a special case. Entire solutions of certain types of non-linear differential equations are also discussed.
Citation
Ping Li. Chung-Chun Yang. "When an entire function and its linear differential polynomial share two values." Illinois J. Math. 44 (2) 349 - 362, Summer 2000. https://doi.org/10.1215/ijm/1255984845
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