Uniqueness of entire function and its linear differential polynomial
Serdica Mathematical Journal, Tome 50 (2024) no. 2, pp. 173-182
Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library
In this paper we investigate the uniqueness problem of entire function \(f\) and its linear differential polynomial\begin{equation*}a_{k}\left( z\right) f^{\left( k\right) }+a_{k-1}\left( z\right) f^{\left(k-1\right) }+\cdots+a_{1}\left( z\right) f'\end{equation*}sharing an entire function \(a\equiv a\left( z\right)\) counting multiplicities(CM) with\begin{equation*}\sigma \left( a\right) <\sigma \left( f\right)\end{equation*}under some restrictions imposed on the coefficients \(a_{j}\left( z\right) \left( {j=1,2,\dots,k}\right)\). Our result improves and generalizes some earlier results.
Keywords:
order growth, entire function, value sharing, linear differential polynomial, 30D35, 34M03, 34M05
Biswas, Manab; Pramanik, Dilip. Uniqueness of entire function and its linear differential polynomial. Serdica Mathematical Journal, Tome 50 (2024) no. 2, pp. 173-182. http://geodesic.mathdoc.fr/item/SMJ2_2024_50_2_a5/
@article{SMJ2_2024_50_2_a5,
author = {Biswas, Manab and Pramanik, Dilip},
title = {Uniqueness of entire function and its linear differential polynomial},
journal = {Serdica Mathematical Journal},
pages = {173--182},
year = {2024},
volume = {50},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SMJ2_2024_50_2_a5/}
}