Creating limit functions by the Pang-Zalcman lemma

Abstract

In this paper we calculate the collection of limit functions obtained by applying an extension of Zalcman's Lemma, due to X. C. Pang to the non-normal family {f(nz): n ∈ N} in C, where f = Re^P. Here R and P are an arbitrary rational function and a polynomial, respectively, where P is a non-constant polynomial.