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. 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.
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