Commun. Korean Math. Soc. 2018; 33(2): 495-505
Online first article April 12, 2018 Printed April 30, 2018
https://doi.org/10.4134/CKMS.c170170
Copyright © The Korean Mathematical Society.
Goutam Kumar Ghosh
Dr. Bhupendra Nath Dutta Smriti Mahavidyalaya(The University of Burdwan)
The uniqueness problems on entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results on this topic have been obtained. In this paper, we study an entire function $f(z)$ that shares a nonzero polynomial $a(z)$ with $f^{(1)}(z)$, together with its linear differential polynomials of the form: $L=L(f)=a_{1}(z)f^{(1)}(z)+a_{2}(z)f^{(2)}(z)+\cdots+a_{n}(z)f^{(n)}(z)$, where the coefficients $a_{k}(z) (k=1,2,\ldots,n)$ are rational functions and $a_{n}(z)\not\equiv 0$.
Keywords: entire function, rational function, uniqueness
MSC numbers: 30D35
2024; 39(1): 105-116
2023; 38(2): 525-545
2023; 38(2): 377-387
2021; 36(4): 729-741
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd