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.

Viewing alternatives

Item Actions

Export

About