TITLE

# Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives

AUTHOR(S)
Jianming Qi; Feng Lü; Ang Chen
PUB. DATE
January 2009
SOURCE
Abstract & Applied Analysis;2009, Special section p1
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We use the theory of normal families to prove the following. Let Q1(z) = a1zp +a1,p-1zp-1 +ãƒ» ãƒ» ãƒ»+ a1,0 and Q2(z) = a2zp + a2,p-1zp-1 + ãƒ» ãƒ» ãƒ» + a2,0 be two polynomials such that degQ1 = degQ2 = p (where p is a nonnegative integer) and a1, a2(a2â‰  0) are two distinct complex numbers. Let f(z) be a transcendental entire function. If f(z) and f'(z) share the polynomial Q1(z) CM and if f(z) = Q2(z) whenever f'(z) = Q2(z), then f â‰¡ f'. This result improves a result due to Li and Yi.
ACCESSION #
55252839

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