A uniqueness problem concerning entire functions and their derivatives

Abstract

We determine all entire functions $f$ such that for nonzero complex values $a\ne b$ the implications $f=a\Rightarrow f^{\prime }=a$ and $f^{\prime }=b\Rightarrow f=b$ hold. This solves an open problem in uniqueness theory. In this context we give a normality criterion, which might be interesting in its own right.

20 pages

Cited by in corpus (1)

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