Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives

Jianming Qi; Feng Lü; Ang Chen
January 2009
Abstract & Applied Analysis;2009, Special section p1
Academic Journal
We use the theory of normal families to prove the following. Let Q1(z) = a1zp +a1,p-1zp-1 +・ ・ ・+ a1,0 and Q2(z) = a2zp + a2,p-1zp-1 + ・ ・ ・ + a2,0 be two polynomials such that degQ1 = degQ2 = p (where p is a nonnegative integer) and a1, a2(a2≠ 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 ≡ f'. This result improves a result due to Li and Yi.


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