Annales Academię Scientiarum Fennicę
Volumen 34, 2009, 157-171


Daniel A. Nicks

University of Nottingham, School of Mathematical Sciences
NG7 2RD, United Kingdom; Dan.Nicks 'at'

Abstract. Denote by B the class of transcendental meromorphic functions for which the set of finite critical and asymptotic values is bounded, and by S that class of functions for which this set is finite. We give some conditions on transcendental deficient functions of members of the class B, including an improvement of a result of Langley and Zheng [10]. This leads to corresponding results for the class S. 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.

2000 Mathematics Subject Classification: Primary 30D35.

Key words: Meromorphic function, Nevanlinna deficiency, singularities, inverse function.

Reference to this article: D.A. Nicks: Deficiencies of certain classes of meromorphic functions. Ann. Acad. Sci. Fenn. Math. 34 (2009), 157-171.

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