Computational Methods and Function Theory 9 (2009), No. 1, 239--253
Copyright Heldermann Verlag 2009
Rational Deficient Functions of Derivatives of Mappings in the Classes S and B
Daniel A. Nicks
firstname.lastname@example.org , University of Nottingham, School of Mathematical Sciences, NG7 2RD, U.K.
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. On the other hand, if 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.
Keywords: Meromorphic function, Nevanlinna deficiency, singularities, inverse function.
MSC 2000: 30D35.
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