Some entire functions with fixpoints of every order

Abstract

In this paper f(z) will always stand for an entire transcendental function of the complex variable z. For p= 1, 2, … the natural iterate f_D(z) of f(z) is defined by These natural iterates are themselves entire transcendental functions; they have been studied by various writers, notably Fatou [3]. References to many papers on iterated will be found in [1].