Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen

Abstract

In this paper it is shown that the functions f(z) = se z are the only nonconstant entire (meromorphic) functions which share two (three) distinct finite values with their derivative. I. EINLEITUNG UND ERGEBNISSE

Notes on Normal Families of Meromorphic Functions Sharing a Set With Their Derivatives

“…Similarly we say that f and g share the value a IM in D if E f ({a}) = E f ({a}). We recall the following result due to Mues and Steinmetz [18]:…”

“…Theorem A ( [18,Satz 2]). Let f be a nonconstant meromorphic function and let a 1 , a 2 and a 3 be distinct complex numbers.…”

A Note on the Brück Conjecture

“…They proved a result in 1977 that if a non-constant entire function f and its first derivative f ′ share two distinct finite numbers a, b CM, then f = f ′ . Since then, shared value problems have been studied by many authors and a number of profound results have been obtained(see, e.g., [5,10] In fact, the conjecture for the case a = 0 had been proved by R. Brück in [1]. From the differential equations…”

Normality and Sharing Values

“…Mues and Steinmetz proved the following result : Theorem 1.1. [7] Let f be a non-constant meromorphic function in the plane. If f and f ′ share three distinct complex numbers a 1 , a 2 , a 3 then f ≡ f ′ .…”