Uniqueness of entire function and its linear differential polynomial

Biswas, Manab   ; Pramanik, Dilip

Serdica Mathematical Journal, Tome 50 (2024) no. 2, pp. 173-182

Résumé

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.

Détail

Keywords: order growth, entire function, value sharing, linear differential polynomial, 30D35, 34M03, 34M05