Abstract
If ƒ is a non-constant entire function which is sharing two distinct values a, b ∈ ℂ with ƒ′, then a result of Mues and Steinmetz states that ƒ′ = ƒ. In this note we consider the case that ƒ and ƒ′ share only one value counting multiplicity, where appropriate restrictions on the growth of ƒ are assumed.
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References
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Brück, R. On Entire Functions which Share One Value CM with their First Derivative. Results. Math. 30, 21–24 (1996). https://doi.org/10.1007/BF03322176
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DOI: https://doi.org/10.1007/BF03322176