Entire functions that share a polynomial with one of their derivatives
After the work of \textit{L. A. Rubel and C. C. Yang}, [``Value shared by an entire function and its derivative'', Conference of Complex Analysis, University of Kentucky (1976); Lecture Notes in Math., 599, 101--103 (1977; Zbl 0362.30026)] the research on the problem of investigating the relation between an entire function and its derivative became popular. The present paper is also an addition in this direction. In the paper the following result is proved : Let \(f\) be a nonconstant entire function of finite order, \(Q\) be a polynomial with degree \(\geq 1\) and \(k\) be a positive integer. If \(f - Q\) and \(f^{(k)} - Q\) share \(0\) CM then \(f^{(k)} - Q \equiv c( f - Q )\), where \(c\) is a nonzero constant.
scientific article; zbMATH DE number 2149311