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.

URL: http://www.heldermann.de/CMF/CMF09/CMF091/cmf09016...

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.

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About

• Item ORO ID
• 22674
• Item Type
• Journal Item
• ISSN
• 1617-9447
• Keywords
• Meromorphic function; Nevanlinna deficiency; singularities; inverse function
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2009 Heldermann Verlag
• Depositing User
• Daniel Nicks