## Entire functions sharing a polynomial with their derivatives and normal families.(English)Zbl 1135.30312

Summary: Let $$f$$ be a nonconstant entire function and $$Q$$ be a nonconstant polynomial. Let $$M$$ be a positive number and $$k\geq 2$$ be an integer. We prove that if $$f$$ and $$f'$$ share $$Q$$ CM and $$|f^{(k)}(z)|\leq M\cdot (1+|Q(z)|)$$ whenever $$f(z)=Q(z)$$, then $$\frac{f'-Q}{f-Q}$$ is constant. Furthermore, we prove the corresponding normality criterion.

### MSC:

 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 30D45 Normal functions of one complex variable, normal families
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### References:

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