Creating Limit Functions By The Pang-Zalcman Lemma

preprint2010arXivOpen access

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}\left\{f(nz):n\in\mathbb{N}\right\} in C\mathbb{C}, where f=RePf=Re^P. Here RR and PP are an arbitrary rational function and a polynomial, respectively, where PP is a non-constant polnomial.

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