Annales Academię Scientiarum Fennicę

Mathematica

Volumen 34, 2009, 157-171

# DEFICIENCIES OF CERTAIN CLASSES OF MEROMORPHIC FUNCTIONS

## Daniel A. Nicks

University of Nottingham, School of Mathematical Sciences

NG7 2RD, United Kingdom; Dan.Nicks 'at' maths.nottingham.ac.uk

**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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