# Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives

• Sahoo, Pulak (Department of Mathematics, University of Kalyani) ;
• Biswas, Gurudas (Department of Mathematics, Hooghly Women's College)
• Received : 2017.05.25
• Accepted : 2018.06.28
• Published : 2018.09.23
• 122 7

#### Abstract

In this paper, we investigate the uniqueness problem of entire functions sharing two polynomials with their k-th derivatives. We look into the conjecture given by $L{\ddot{u}}$, Li and Yang [Bull. Korean Math. Soc., 51(2014), 1281-1289] for the case $F=f^nP(f)$, where f is a transcendental entire function and $P(z)=a_mz^m+a_{m-1}z^{m-1}+{\ldots}+a_1z+a_0({\not{\equiv}}0)$, m is a nonnegative integer, $a_m,a_{m-1},{\ldots},a_1,a_0$ are complex constants and obtain a result which improves and generalizes many previous results. We also provide some examples to show that the conditions taken in our result are best possible.

#### Keywords

entire function;derivative;uniqueness

#### Acknowledgement

Supported by : UGC-DRS-SAP

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