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Rational deficient functions of derivatives of mappings in the classes S and B

Nicks, Daniel (2009). Rational deficient functions of derivatives of mappings in the classes S and B. Computational Methods and Function Theory, 9(1) pp. 239–253.

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Abstract

Let f be transcendental and meromorphic in the plane of finite lower order with a bounded set of finite critical and asymptotic values. It is shown that a rational deficient function of any derivative of f is zero at infinity. If instead f has arbitrary order and a finite set of critical and asymptotic values, then any rational deficient function of f' must have a multiple zero at infinity. Furthermore, if such f has finite lower order then f' admits no rational deficient functions other than 0.

Item Type: Journal Article
Copyright Holders: 2009 Heldermann Verlag
ISSN: 1617-9447
Keywords: Meromorphic function; Nevanlinna deficiency; singularities; inverse function
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 22674
Depositing User: Daniel Nicks
Date Deposited: 04 Aug 2010 11:19
Last Modified: 27 Oct 2012 21:05
URI: http://oro.open.ac.uk/id/eprint/22674
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