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Deficiencies of certain classes of meromorphic functions

By Daniel A. Nicks

Abstract

Denote by <i>B</i> the class of transcendental meromorphic functions for which the set of finite critical and asymptotic values is bounded, and by <i>S</i> that class of functions for which this set is finite. We give some conditions on transcendental deficient functions of members of the class <i>B</i>, including an improvement of a result of Langley and Zheng. This leads to corresponding results for the class <i>S</i>. It is also proved that no derivative of a finite lower order periodic function has non-zero finite deficient values. We show by example that the finite lower order condition is necessary here

Year: 2009
OAI identifier: oai:oro.open.ac.uk:22682
Provided by: Open Research Online

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