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.
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